#1
I need something heavy enough for BEDGBE (for playing Parabola), but something that can still play E Flat. I don't care about bending / soloing. My guitar is 25.5 in.
#2
None exist. A guitar setup for one tuning and string set will not work at another very well, and the lower you go, the worse it will get.

You can try it, but you'll be disappointed by the results. One tuning per guitar for best results.
Guitar/Bass:
Schecter: Damien 6/Stilletto Extreme 5, Squier: Bullet HSS*, Washburn RX10*/WG-587, Agile Septor 727
*mods

Amps/FX
Peavey: Vypyr 30/Max 112 (200W), ISP: Decimator

Quote by dannyalcatraz
Understood- I waste money on amps*, too.

justinguitar.com is the answer
#3
What strings would you use for standard tuning? For your BEDGBE tuning, you could use those, minus the 5th string and add a low 6th. For example if I normally used 10-46, I would try a 10-56 7-string set and chuck the A (about 36) string. The low B might feel a bit sloppy, and the Eb tuning would be a pretty rough compromise on the same guitar, as noted by bjgrifter .
#4
Tony Done I use 10-46s for standard, but that's on my Les Paul. The guitar in question is a shitty Strat clone with a longer scale length (it was my first guitar and it has sentimental value, that's why I still want to use it) I'm currently looking at the Beefy Slinky 11-54s and I think they're going to do the job. Thank you for your help though.
#5
Give it a shot. Longer scale lengths (say about 27"+)  tend to use 9 gauge strings on the highs, but then I understand jazz players use 13 gauge sets for standard tuning, If you can't reasonably mess with the bridge, you might need something for the low-B. I haven't had good luck on a low B with something under 56 gauge with a 25.5" scale, but your mileage may vary. 
Guitar/Bass:
Schecter: Damien 6/Stilletto Extreme 5, Squier: Bullet HSS*, Washburn RX10*/WG-587, Agile Septor 727
*mods

Amps/FX
Peavey: Vypyr 30/Max 112 (200W), ISP: Decimator

Quote by dannyalcatraz
Understood- I waste money on amps*, too.

justinguitar.com is the answer