The flow through 3/4" is nearly double that of 1/2", so run 3/4" to your 3/4" valve. Pex is too restrictive for your application - while the outside is nominal for 3/4", the inside is barely bigger than 1/2" copper since the wall thickness is greater. You don't want any hoses in that connection. I'd solder it. You can buy heat shields to aid you in keeping heat away from parts you don't want to. Keep a spray bottle of water around, too. If you are not comfortable, a plumber might be a cheap alternative to ruining the tub.