I have thought about this in regards to combining stannous fluoride with hydroxapatite due to the synergy between fluoride and hydroxyapatite (Although I believe most studies which have found this synergy used sodium fluoride, not the traditionally superior stannous fluoride, so not sure if the synergy will uphold). I think there are only a few toothpastes on the market with a proper concentration of both sodium fluoride and hydroxyapatite, have not seen any mouth rinses with both. The problem with mixing mouthrinses or toothpastes is that you will inevitably reduce the concentrations of both active ingredients, in absolute quantity they will be the same, but I wonder if they will become overwhelmed and nullified by the relatively larger quantity of non active ingredients. IIRC hydroxyapatite in toothpaste is rated 10% max in EU, and it's also most effective at that amount, for mouth rinses it is 0.465 %. It would actually be easier to find some high fluoride toothpaste that would suffer less from dilution, I've heard recommendations of around 1500ppm, so if I am not mistaken getting a 3000ppm toothpaste would allow for ok dilution if only you had another with 20% hydroxyapatite in a 1:1 ratio. Overall the solution I am settling on is fluoride rinses when waking up and going to bed, and hydroxyapatite toothpaste twice a day, no clue about the synergy there, but seems reasonable as most hydroxyapatite pastes are filling the no fluoride market niche, which comes with the nice benefit that they aren't filled with a bunch of other trash inactive ingredients, meanwhile fluoride mouth rinse less affected by such things compared to fluoride toothpastes.
Be carful using high PPM fluoride. Too much fluoride can cause white spots to appear on your teeth. (I believe the dentist can clear the spots, but don't quote me on that)