Hi Wolfsbora,

You seem fairly handy, and it sounds like you have some experience soldering, so you might want to go ahead and try replacing them yourself.  I'm assuming you understand that capacitors can hold a lethal charge, and how to ensure they are discharged before servicing.  

My suggestion is to buy the replacement capacitors, make a plan, and execute carefully.  Let us know how it's going, and post if you need help.

Best regards, and happy new year!
I suggest reading up more about how capacitors work. Forget about the .1 uF "grounding" cap. It will attenuate most of your signal. Go with the .022 uF tone cap for more treble. The punchy mid-range sound can be dialed in with your amp's EQ/tone stack.
Cool project! I have played around with space-charge tubes as well. I built a battery-powered amp, too, using a 12V 7AH SLA battery. Here's a short video testing a particular version using two 12K5 in a push-pull configuration, with the gain sections using all four triodes of two 12U7:
Acquiring a DMM and learning how to use it will help as well.
I have an Associate's degree in Electromechanical technology, and worked my way into an engineering technician position after 12 years of building, repairing, and designing equipment. Engineers spend most of their time designing and calculating/modeling, whereas electronics engineering technicians do the hands-on work of building, testing, and re-design. To earn an Associate's degree, you still must learn the same fundamentals as an engineer, but don't get as deep into theory. I think if your goal is to design and build amps and effects, an Associate's degree would be more advantageous than a Bachelor's. Other advantages are less time to earn the degree, and lower tuition. If your amp building business doesn't work out, the degree will open doors for you in technological fields.
Here is a reverb driver I came up with awhile back. Note the mistake with the two "X's". The input of the reverb through the 1uF capacitor should be connected to the emitter, not collector. The transistor can be a 2N4401, 2N3904 or equiv. For the op amp, I used 1/4 of an LF347, but any audio-oriented op amp should work. VCC was 12V, but 9V should work. Good luck!

Replace the capacitor. Also, check the rectifying diodes and power transistors for shorts. Check all solder connections; could be a heat-related poor connection, which may be why it works fine at first, but acts up after it warms up.
Smoke usually means burned component/trace/wire, etc. A blown fuse means overload, which is also indicative of a blown or shorted component/trace/wire. Sound more like internal component failure rather than a bad tube.
That radio needs a lot of work to make it safe. The rest of the paper capacitors and cloth-insulated wiring should be replaced. As far as figuring out what tubes go where, you need to determine which sockets are for the power, audio, and RF. Don't start a fire or zap yourself!
You won't need the crossover. If used, it wouldn't necessarily sound "bad", just different. The purpose of a crossover is to filter certain frequencies from the speakers in a system. Speaker sizes are intrinsically more efficient at reproducing a certain range of frequencies. Smaller speakers are better at reproducing higher frequencies, and larger speakers lower frequencies. Guitar and bass speakers are designed to reproduce guitar and bass frequencies. Playing a guitar through a speaker designed for bass will remove much of the middle to high frequencies that would be more prominent with a smaller speaker. The lower frequencies will be more pronounced. Some people like that sound, some people don't. Depending on your amp and the speakers' impedance, you may or may not be able to connect the 8" speakers to boost the mid/high range.
Looks to me like all he did was replace the power jack and blue LED. He also doesn't understand that the Pedal Power outputs 1-4 are only rated at 100mA, which is why those outputs can't power the Line6 pedal.
Try connecting two or three .0047uF in parallel (both leads of the caps connected together). Two .0047 will be close to .01, and three in || will be close to .015.
Gear picture upload doesn't work for me. It starts, then after about 5 seconds, displays, "File has NOT been uploaded!" Never gives a reason why. Picture is JPEG, 700 X 933 pixels, and 726 KB.
Increasing the cathode resistors' bypass capacitor values will also increase the AC gain.
Get an Ibanez or Schecter for drop C metal. Keep the Strat for standard blues and rock.
Or, find an old smoke alarm, alarm clock, or microwave... basically anything that beeps.
You might want to add some shims the same thickness as the "pushlift" height under the chassis to keep them from being pushed in. Or, a couple of battens on the ends of the chassis might work, too.
I always love following your builds. It's looking great! I wish I had more time to work on my own stuff (too much time wasted repairing other peoples' shit, lol). You should seriously think about starting an Ebay store or something.
The Tremol-No keeps the bridge from moving with thumb screws. You loosen the thumb screws to release the bridge. I have one on my Damien FR. Works pretty well, but the strings still detune during big bends. Probably won't need it with a standard Fender trem, but it's your party.
Good job, man! Interesting circuits. You stole my "LED mounted to center of tube socket" idea :-P I know how challenging it is to fit everything into a limited enclosure. I also can't wait for the clips ;-)
There's an ass-load of information at your fingertips. Here's a decent Youtube video:
3. The Tremol-No works OK. Not as solid as blocking the trem, but gives you the option to quickly switch between fixed and floating bridge. I made stainless back covers for my Schecter Damien FR. I milled a slot in the trem cover for easy access to the Tremol-No thumb screws.

Wrecked 'em! It should have been easy to heat the pad with the soldering iron, and pull the lead out of the hole. I hope you learned from your mistake.
A better quality picture would really help.
What kind of tone and genre are you going for? Since you are getting an 8 string, I'm assuming death metal or similar. I use Eminence Patriot Screamin Eagle for hard rock and metal. They sound great with my Ibanez 7 string tuned to standard B. I acquire them from Parts Express. They have a nice selection of Eminence.
^ Right, if you're going to drill into the shaft of a drill bit, you need a drill that is harder, like carbide. If there's some material sticking out of the wood, your best bet is a decent pair of vice grips. If the break is flush with the surface, drill material away from the larger drill's flutes with a smaller drill, but don't breach the diameter of the larger bit. After that, use needle nose pliers to grip the flues and pull up while turning counter-clockwise.

How the hell did you break a drill of that size in a piece of wood?
Doesn't anybody know how to use Google? I typed "install a floyd rose" and this was the first hit:
What you should have done was cut one of the resistor leads in half, and bent the lead halves apart a bit. If it didn't work, it would have been an easy job to solder the leads back together.
What, the resistor? An ohm meter would tell you.