The want for an accessory rail is the killer requirement for many of the off the shelf guns on the market. If you drop that requirement, almost anything will work. If you are willing to put your own accessory rail into a stock, or simply screw your hamster to a stock, it opens more opportunities. Also, you intend to shoot hunter FT, and never shoot WFTF/Open? If so, consider you may not need a hamster. In hunter division, you cannot make any stock adjustments after the first record shot, that includes changing anything related to the hamster.
There are aftermarket stocks or accessories available to add accessory rails.
I am personally not a fan of the bullpup design for positional target shooting, which although I am sure the ghost, FX Impact, and other similar guns are accurate and great shooting guns, the design does not work for me.
Add your own rail to a wood stock, assuming there is enough stock available to do it. You will need to mill the stock to make this work, so might need to find someone with the right tools if you go this route. Here is a place to get a rail.
https://freelandssports.com/product/anschutz-blank-rail-section-15/ If you can find them, the ACZ FT (CZ Aeron) stock for a FX Dreamline Classic has a rail on it.
https://utahairguns.com/acz-ft-chassis-fx-dream-classic-streamline/ . Utah Air is currently out of stock on these, but seems like a nice stock.
If you like the FX Impact, this ARCA rail is similar to the UIT rail.
https://utahairguns.com/kraford-lypt-fx-impact-arca-rail-gen-3/ Single shot loaders are available for many different guns from CARM Magazines.
https://www.carm-magazines.com/carm-magazines.aspx