In my (limited) experience the Taylor basses had incredible craftsmanship and sounded great acoustically on the A, D, and G string, but the E string disappeared. My impression was this was caused by the port tuning of the resonant cavity. Because of the unique nature of the design, I would think mic'ing the bass alone and getting an even sound across all four strings would be very challenging. Obviously finding the right mic placement would be the first thing to work out. The trick is to find the right distance and point to aim the mic at so you get even tone, high light the qualites you like, and minimize the qualities you don't like. The choice of mic and the acoustic properties of the room are important issue that will factor in significantly to the final sound you get.
The Peluso 22 251 Frequency response appears to be flat from 40hz to about 1.5khz where it begins to rise. I suspect that rising HF response will cause problems as ABGs tend to produce alot of mechanical noise, so I suspect you will need to do a lot of work on the upper mids to compensate.
Also the boxeyness of the bass is most likely because it doesn't produce enough low frequency energy to give it a deep sound. Unfortunately due to the low volume produce by these instruments, if you scoop out too much of the low mids, there will not be much left to work with. You could try a very soft broadband dip in the 400hz region and small broadband boost around 80-100hz. Just a few db either way. The boxeyness could also be a symptom of the recording space.
I have a Tacoma Thunderchief. Acoustically it's one of the louder ABGs that has been made, but I would say the tonal quality of the A, D, and G string pale in comparison to the Taylor. Acoustically these three strings on the Taylor sound rich, deep and resonant. The Tacoma is far more even across all four strings, but I don't think it would sound great mic'ed.
If I were recording the Thunderchief, I would actually use a small amp and take a DI of the signal. At a certain volume, the interaction between the amp and the Thunderchief are just magic, and the magic translates pretty well through a DI. Some tuning with the built in preamp is useful to even out the tone a bit. Also the cost of the Tacoma's loud acoustic volume is it doesn't cope with high SPL very well, so finding the sweet spot with the volume is key. I have never owned a Taylor, and I can't remember if I ever plugged the one I played into an amp. But I would give this approach a spin.
Another option would be to try a hybrid approach where you use both a mic and DI. As you probably know, you will need to do a bit of time/phase alignment in your DAW for the two sounds sources to integrate well.
