IMHO: Run the BT39SS if you can afford to. they are about the same size as 2.75 - i wouldn't be scared off by the min rec rim width. We run the 2.5" x 18" on MB5s and they are skinny by fantastic even in the wet. They have done very well on the CVMP track on French bikes (as have the Sava slicks).
cheap enough straight from japan. https://japan.webike.net/products/1688200.html
the next step toward slicks on moped sized rims is going to be the 90/580 Battlax v02 https://japan.webike.net/products/21721792.html
they are significantly wider - but moto3 spec slicks. you will most likely want appropriate rims to ensure the correct contact patch size and location to get the most out of them.
with the right rims you can run the dunlop KR189 rains. bikes aren't heavy or fast enough to shred them in the dry, and offer crazy grip.
Good tires will flush out weaknesses in your frame and suspension as you corner more aggressively.
tracks like CVMP won't push that limit as much because of the lower speeds.
SO, I think you would be fine continuing your program with heidenaus - i think they are more substantial than gp-1's which have a wimpy sidewall.
but if you got the BT39's you would not be disappointed and I think it would be a good low risk, high confidence investment.