Well, I back my tractor on. Cause my ramps just meet the front tires, I think it is a better deal if the back would fall off when going up the ramp. At least then I would land level. The concern about the hood is defintely justified when pulling it backwards, not to mention the seat trying to flip up. Implements do make a differnce for front/rear loading options, whatever makes your load right is the best option.
Chains are good, but often are over kill in my opinion. However, if you are using straps, make sure you get straps with a load limit as close to the weight of your tractor (ok this may be over kill, but if one strap would fail the other ones have to make up for it). Personally I completely ignor the break strength since they always appear to be so dang high. Axle wrap straps can be very handy, and I like to use them for those places where you can't put a hook.
If you go with chains, be sure to get proper strength, I actually had a hard time finding binders strong enough, had the correct size hooks and finding chains that would do the job. On top of that, extra chain is harder to deal with then extra strap. Straps that are properly secured won't slip. Straps do wear over time, but they are a lot easier to use.
As for cris-crossing th traps to prevent slipping, I don't see where that would do much different then securing 4 opposite corners (assumming your straps are tight. On higher tie down points it does help for stability or maybe on vehicles with suspensions, but on a tractor, I have never had it slide any direction.