Mr. 16 I think you've answered your own question to a degree simply by the act of asking it. You are obviously willing to consider the option of renting/borrowing so I think the practical advice is to do just that. It will make your travel easier, will cost a less, and this adds up to more than you think! By the time you spend time and gas looking/shopping, getting optics on it, ammo to site that in, Ammo cost in general. Firearm permits. The travel case needed. I may have gone overboard a bit, but when I added up the 4 new guns (the two we started with ended up with relatives moving in!), 2 double cases, soft cases, cases of hard to find ammo, decent optics, some clothing and boots, we spent $12,000 for two of us!
Obviously a lot of guys on here (myself included) are a bit infatuated with our guns! But you may be more about the hunt and not as hung up on the gun.. That can be your advantage so go with it rather let us all talk you into a gun with our machismo.
I would highly recommend you get details on what is available to use and ask for detailed pictures, especially of the optics mounting. You don't want to get there and find out you have to contend with scope mounting that you can't see out of. Hopefully the outfitter has a couple choices... Then try to set up your 338 similarly even if you need to buy another set of scope rings.. Practice with that will suffice very well and you will have a great hunt being able to spend at least $2-3000 more on trophies than if you go out and buy even a low cost gun and mid range scope.