#1
I own a Fender Blacktop Baritone Telecaster that with 12 gauge strings. I like being able to tune low without string flapping, the larger frets (my hands are kind of big), as well as the increased control over what strings get bent/plucked. I also have been practicing with it in standard E tuning because it gives my hands a great workout (if performing I play with 11's, and if it's a guitar with 25" neck the tension is even less which I find an ideal tension for performance).

Reading some posts however I'm worried that standard tuning with 12's on a baritone guitar might be too much tension for the neck. Are there any modifications I can make to ensure the guitar doesn't warp under the tension, or are 12's in standard E tuning completely out of the question for baritone's (and if so, would 11's be ok?). It is currently my only guitar so never tuning to standard E isn't really an option for me (for practicing). If I should never tune it to standard E unless with light strings (<10), I will probably have to trade it in for another guitar, suggestions are welcomed for a good fit for someone that has larger hands and likes strings on the heavier side. Thanks in advance!
#2
Is there any reason you can't tune it down at least a few half steps? D standard, for example. Will play just like E standard.

Having a really strong fretting hand isn't all that important. For some, it might even be a bad thing because they might subconsciously apply too much pressure to strings with less tension, causing the pitch to change.
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#3
I often play along with 'jam tracks', or practice songs with my son in Rocksmith, which requires original tuning, I guess I could capo but would rather not if possible. I agree that it can be detrimental at times, when I pick up a guitar with 9's I definitely fret too hard causing pitch changing, or overshooting bends. But I feel like I can transition to a lighter touch fairly quickly if needed.

I use the extra tension not so much for fretting but for bends in leads that are often a stumbling block for me (partly because I like heavier strings to begin with, < 11's just feel too flimsy for me and I think gives too thin a tone, and I constantly break higher strings) . My fretting hand gets tired with successive quick bends (i.e. freebird solo), bending + vibrato was always challenging too. If you think I'm going about it wrong I'm all ears, it just seems like an effective way to build strength while practicing.