I don't think it's hand wringing, I think it's the conservative nature of this bunch and our general looking out for each other.
Personally, I'd be pretty hesitant to (1) put so much weight on the rear mount - especially if it's offset by a bikerack (increasing the lever arm of the weight); (2) especially back there (as in, the single worst place to add additional weight if you're seeking to reduce trailer sway/wag).
The 300lb rating for the rear mount (while frame mounted) is likely AT the mount end. Adding ~200lbs, and then offsetting by the width and height of the loaded bikerack's center of gravity will multiple the force that the deadweight has by the distance from the COG (where the weight is on the rack) to the mount. I'm going to guestimate that the COG is going to be a foot out and a foot up, putting the leverarm at 1.4'
1.4' x 200lbs = 282.8 ft lbs of force.
It's not straight out, though, so - in this case - gravity will be helpful (won't be as harmful) until the trailer starts to see some up and down motion (which will increase the force of the load. At least the rack is a low/platform type, which will keep forces somewhat tamed, as opposed to the hanging type that are more favored for bicycles.
200lbs out back isn't the best place to mount it, and you will be reducing your weight back there by migrating the spare tire (somewhat reducing the polar moment of inertia that is so happy to make the trailer sway). But still, it gives me pause.
WV_Mountaineer, after looking at all the above, I'd suggest you pack the bikes, folded, in the truck bed and leave the trailer tire where you have it. Alt: load them in the body of the trailer over the axles. You might also check your truck's payload sticker and do some quick math to make sure you're still within spec. SEEMS LIKE YOU ARE, just want to doublecheck.
Your Roo is going to be a lot of fun, so glad you checked in here and are trying to be careful. As you gain experience, you'll learn the impact and effects of what loading choices you make have on the trailer. No matter what, the old adage is always true: slowing down reduces the problems that are magnified by speed.
I hope to see a lot more of you around the boards, friend!