I always liked some of the Rola units, but without some sort of lower crossbars or mounting options, they always looked goofy sitting above the OE crossbars. Beyond that, I'm not much help for alternative basket options.
However, if you're looking for a lower profile "base rack" design with a ton of mounting provisions, consider some of the aluminum extrusion racks out there. They're pricey, and while some probably won't even fit our trucks without custom brackets, Prinsu universal racks (https://prinsudesignstudio.com/category/universal-top-racks/) and Smittybilt Adjust-a-Mount brackets (https://www.amazon.com/Smittybilt-AM-4-Mounting-Bracket/dp/B00AQFE8BG) might be a viable option...albeit a $900 one, after tax, shipping, and some additional hardware.
To that extent, my buddy @Rockit and I are in the process of making our own base racks out of extrusions that are made-to-order (cut-to-length and machined for assembly). I was planning to start a new thread on the topic when both racks were complete, but maybe some info here/now might spark some ideas. Cost-wise, we're also well under half the cost of the Prinsu setup, with a result that'll fit our exact needs.
These slotted extrusions are great because you can mount practically anything, anywhere, and there are already a bunch of off-the-shelf accessories for Rotopax, Hi-Lifts, etc (Prinsu has a full line-up of them). I'm fabbing up all our mounting and accessory brackets, like awning mounts and lighting tabs, but also have some ideas for other items. But these racks are far more versatile options than any basket I can think of. They're also lightweight, extremely strong, and corrosion resistant. Cost is a little higher than an off-the-shelf basket might be, but the versatility makes it worth it.
For Rockit's QX4, we're doing a 50"L x 42"W x 2"H rack using 2"x1" and 1"x1" quarter-round extrusions, with the LH side being 72"L for full awning support, like so:
I made some brackets that'll get the rack about 1" off the center of the roof (the height varies because of the curvatures F/R and L/R on the roof), and around 1.5" at the corners. The brackets are also slotted so the rack can be raised another inch if we need clearance anywhere, or to level it out:
Since I have an SE roof rack, mine will be a drop-in rack that's 52"L x 36", and uses 2"x1" and 1"x1" extrusions: