Getting 2 types of tires
 

I have a 2016.5 CX-5 GT AWD. One of my tires had a hole in the sidewall, so I need a new one. There is barely any wear on the tires so I should be able to just get a new one and it would work fine with the other 3 existing ( > ~6k miles, and tread checked at the tire shop). However I the tires are the Toyo A23 225/55r19 and they are back-ordered at the factory, and no one has one in stock, apparently it will be months before a new one comes in. Currently I have snow tires on and need to change them out since I need to drive cross country and don't care wear away the tread on the snow tires.
However I can't afford 4 brand new tires. Various people have suggested I would be OK with getting just 2 new tires (new as in same size, but different brand/model). so 2 of the Toyos on 1 axle, 2 of something else on the other.
The tire shop guy said this might work, but to check with Mazda to make sure it won't damage the drive train. My instinct is it should be fine, since I am under the impression that the tires all rotate independently, and the difference in the tires shouldn't be that great, even if they are different manufacturers.
Asking here for thoughts (I emailed Mazda but waiting on a response)

As long as the treads are similar, the construction is the same, same size, then at 6,000 miles you will be ok. I've never seen any issues with CX-5s having transmission or driveline damage due to tyres, but it's better to be safe than sorry.