What is the most dramatic way of increasing a speaker's Bass and Low mid?

Modify your crossover.Or source a xover which has the specs you wish.
cheaper way, increase the cap value on the low mids

About 10 years ago I bought a pair of Thiel CS1.6, my first new speakers since the Mission 700s I started with 20 years earlier. Reading around I came across the "Sumiko Masterset" method for placing speakers and decided to give it a try. My first attempt ended with the speakers a little over 2 feet (64.5cm) to the wall behind though I went for only a small amount of toe in. As I gradually got used to the system it became more and more apparent that the upper bass/lower mid was a bit lacking so I had another go and found another node 22cm closer to the back wall that filled in that region but at a small cost in soundstage depth (which I could live with). I've since moved the Thiels to a much larger room (from 13.5' by 12.5 to 23' by 19')' and after I'd got them placed to my satisfaction discovered they were again 42.5cm from the wall, coincidence? In both cases the wall is solid, I've never had to deal with a plasterboarded wall behind speakers.

"You can't fix what you can't measure" is what we say in QA.

Get a calibrated mic and Room EQ Wizard software (it's free!) and measure your current system.

My guess is you'll be appalled.  Most systems sound TERRIBLE in actual rooms.  (Check out the in-room frequency response graphs in Stereophile reviews for further examples)

Experiment with speaker placement.  Sometimes small movements make big differences.

My answer is "digital room correction" - my music is PC based and I use the free MathAudioRoomEQ plugin for my music server.

The Lyngdorf is a hardware based system that does similar.  There are others, including Dirac Live.

I'd at least audition some of these.  Measure the results with your mic and RoomEQWizzard software.  Decide if the trade-offs are worth it.

For me there's no question about it - I rent and have hard limitations on which room the stereo can be in and how I can treat said room.

You may find your answer through dedicated subs or, if you're lucky, better speaker placement.

It could be your room, you know. Read F. Alton Everest texts to learn about room modes. If you have a square or other poorly proportioned space no amount of gear at any price will solve this. As suggested by others, change your listening position. Mr. Everest will help with that and you may need to move more air with a sub. 

I haven’t read though the entire thread but, try high quality room treatments. I highly recommend the Stillpoints Aperatures.

Still, in this day and age, most people would rather trade a component for another at a loss/on top of a big extra expense instead of taking the time to try room treatments. Some have mentioned trying a Lyngdorf. My feeling is to get as far as you can go passively.This is the best path.