With the method I described it doesn't make a difference what kind of device you want to hook up as long as it has analog input and output jacks. It's a generic way to route a signal from a DAW on the Axe grid, out to the exernal device, and back into the Axe so that it can be recorded in the DAW again. It should work for what you're describing unless I misunderstand something...
I want to take that clean DI and reamp it through the AxeFx (with a different amp tone) ideally using the USB cable. And to get the reamped guitar back into Reaper, I want to run it via the OUTPUT of the AxeFx and run it back through the API 312 preamp so I get the same sort of API flavour on top.
Maybe a more specific example would help. Let's say you want to reamp the DI signal with an Amp + Cab block and no further effects, send the reamped signal out to the API preamp for some shimmer, and then simply record whatever comes out of the output of the API. To do so, simply build a preset with the following two signal chains:
In1 -> Amp1 -> Cab1 -> Out4
In2 -> Out2
The first signal chain processes the DI signal and then routes it to an output jack so it can be sent to the API. It doesn't matter which jack, I picked Out4 here as you're probably not using it for anything else at the moment. The second signal chain from In2 to Out2 is just there to allow you to record the analog signal returned from the API into Reaper, as your inputs in Reaper correspond to the Axe output blocks. For this part, you can also use any free input jack instead of In2; however you must use either Out1 or Out2 as the output block as only these outputs can be recorded via USB.
Now simply run a cable from the Axe Out4 L jack to the API input jack and another from the API output jack to the Axe In2 L jack, and don't forget to turn up the corresponding front panel output knob.
That's the Axe and API side of things taken care of. Configure Reaper to send the DI signal to the right ASIO output (#5 / "Input 1 Block L"), and configure the Axe I/O setup to route that signal into the In1 block (Digital Input Source = USB Ch 5/6, In1 Source = Digital). Add a track in Reaper that records the right input (In 3/4 for Out2 L/R), and you should be set.