Here is a Weaver T36 mounted on scope blocks on a CPA half barrel that has 1.1" flats and 1.0 inch round.

Sorry my action is having a RKS  22 barrel installed so I can only show you the barrel by itself.

With the normal scope blocks the Weaver scope is too far forward for proper eye relief (and no play left to adjust scope rings). Also on the blocks the front is a bit close to the barrel and would require higher blocks or higher scope mounts.

Ideally to mount a Weaver you need a raised scope base that juts back over the receiver so you get proper eye relief. Sounds like you have ordered the right set up from Gail. With the right scope block it does not matter if you have a half round or a full round barrel. Depends on what you prefer aesthetically.

The modern scope I prefer for my CPA is the Unertl 15X Ultra Varmint.

On my CPA barrels (I have 2, oct/round, 1.1" @ muzzle), with Weaver T-36 scopes, (on the CPA modified Weaver mounts) I prefer to use the Burris Signature rings with inserts allowing elevation and/or windage adjustment at the time of mounting; thereby retaining full adjustability of the scope as needed on the bench. My "dead wind zero" is nearly at the center of the scopes' adjustment range before fine tuning. Another advantage of the Burris inserts is that they are made of a firm plastic and will not leave ring marks on the barrel.
You might also consider having CPA provide a front sight dovetail to allow you or a furure owner to shoot either or both Iron sight and/or Any Sight matches. (Personal experience.) Good shooting. You won't be sorry you went with CPA. You'll have a winner out of the box. Load development and bench technique may take some time; but, the rewards will be great.