Goo gone will not do anything good for the stock. For a plastic stock, it'll likely eat the stock plastic, or at least, denature the plasticizer or stabilizers, so you'll ruin the stock. For poly coated wood, it'll likely eat the urethane coating, or again, at least degrade the stabilizer. For oiled wood, it may stain, darken, or lighten the wood, or at least draw oil from the stock which may be difficult to replace for an even finish. It could even denature the wood and cause a "dry rot" type appearance in short time following sun exposure. The harshest solvent I would use on almost any rifle stock is isopropyl alcohol. If you're OK with fully stripping and reoiling the stock, mineral spirits would get it off, but again - it's a heck of a job to redo the finish just to remove a little tape goo which should come off with some dedicated time with rubbing alcohol. You will need to reoil the stock after alcohol as well, but it will be much more uniform than the harsher solvents, and much easier to reoil.
As for the BDC reticle: any BDC really isn't accurate for more than ONE particular combination of ballistic coefficient, velocity, and environmental condition, so even if you were shooting a 223rem, it's VERY likely the reticle would not actually match up with your trajectory. You're ALWAYS stuck trying to learn the relatively random yardages which correspond to your reticle, and then still have to do that relatively random math based on yards, rather than using a proper milling reticle to work directly with your trajectory instead of the ranges. I'm not a fan of BDC's, but you're not disadvantaged in using a 7-08 with it any more than you would be with a 223.