Everybody is an expert, yet none of them have actually offered real world experience towing the trailer you are asking about with the truck you have. I basically have the same truck and I tow a Fuzion 315 which is almost identical to the Raptor 300mp except it is 14" longer.
The pin weight on the 300mp is a couple hundred pounds lighter than the 315, but again they are close. There is no doubt that the 300mp will be maxing out your truck. I always hesitate to say you are safe because I have no idea what kind of driver you are or what your experience is. I will say that you truck is more than capable of handling that trailer. I added airbags to help improve the ride, but the truck does sit level without the bags.
People get all caught up in the "the load in the garage will take weight off the pin", but it doesn't seem to work that way with long 5th wheel haulers. It seems to have a much greater effect on bumper pull haulers. With about 1200 lbs of cargo (golf cart, etc) in the garage, it shifts about 60 lbs off the pin. The fresh water tank is directly over the axles and doesn't seem to affect pin weight when it is full. The black and grey tanks really affect pin weight when they are filled. I try to travel with those tanks empty unless I absolutely can't avoid it.
The biggest thing you will need to worry about with your truck is the rear tires. If you have 18" wheels, your tires are probably not rated for the load they will need to carry with the 300mp. The 20" tires are rated a lot higher and their shorter sidewall results in a lot less squirm or sway. Fully loaded, the 300mp is going to put your rear axle weight somewhere around 6600-6700 lbs.
As for the garage, you may be able to use the top bunk if you remove the bottom bunk depending on how your bikes are equipped. The top bunk only has less than 60" clearance in a sleepable position. People get by with Harleys and a 10' garage but it isn't ideal. Unless you can squeeze the bikes 3 wide into an 8' wide space, they aren't going to fit in the 10' garage. Even if you could squeeze them in 3 wide, I think you are going to exceed the weight limit of the garage. You really need a 3 axle trailer with a 12' garage for that load. We settled on the Fuzion 315 because it was the biggest trailer that a SRW truck should be towing. It meets our needs but just barely. I would really like to have a 12' garage, but that will have to wait until I get a dually in a few years.