Please Help Weed Them Out

Just a word of warning. Most preamps with headphone outputs have extremely inferior ones. I don’t know this for certain about the Benchmark, but it is very, very likely. It takes a lot of effort / cost to produce a good headphone amp (think building an amp). You can see my current headphone system under my user ID. I took me over ten years to learn / assemble a great headphone system My headphone amp produces enough current to power speaker.

Given the poor quality of most preamp outputs (in particular, lack of current) I would recommend getting headphones that are very easily driven. There are two that come to mind Focal and Ultrasond. Go as high up (think used) as you can go.

I understand your warning, but the Benchmark puts in a separate THX Headphone AMP of very good quality. At least good enough to be called decent. 

Yes - the Benchmark HPA4 does have an excellent headphone amp. Certainly up there with the best.

I would consider the AKG K371. Closed back and can be had for less than $300. Definitely has the bass you're looking for. It's my daily driver.

OK, so I got a set of AKG K371. I like them a lot, and only $160 from Amazon! I originally got a set of Hihiman HE-R9, but I thought they were too dull sounding and very bulky. These AKG' are great, and I just ordered a set of Dekoni Choice Leather pads to try. I'm actually considering stepping up my game here. What headphones would anyone recommend with a similar sound signature, but way better? By way better I mean in the $1,500 to $2,500 range.

Would open-backed models be a possibility or do you need closed?