Personally, I would not waste my time sporterizing an old military rifle. The Enfield or german Mausers can be used as platform receivers for target rifles, but that sort of rebuild is MUCH more intensive than what you're talking about.

Old military rifles, if they're the genuine article and in good condition can have high collectors value, so sporterizing them will RUIN any value they had.

Secondly, yes, they're heavy, but even with a modern synthetic stock, they're still heavy than a typical modern rifle. At the end of the day, it's still going to be an enfield. It'll still be long, still heavy, still have way too long of bolt throw, and probably a lot of slop, still have a heavy trigger, etc etc etc. It's like putting a flame paint job and a bolt on "lego block" race spoiler on a 1975 pinto. It wasn't all that great in original form, and now you just made it look even more stupid.

Plus, if you consider that the scope mounts, bending the bolt, new safety, and new stock will cost you about $100 a piece, you'd be saving money to just go buy a modern Savage bolt action and call it a day.