Unsurprisingly, the Bo and Mooney crowd has chimed in. Bonanzas are nice, but a Bo in your price range (as already mentioned) is going to need a lot of TLC (read: $$$). Pay me now or pay me later. Mooneys are great, but also already mentioned are the potential compromises on space and/or useful load.
Regardless, your most efficient path to more speed is a retract. In your price range, that's a 182RG, Commander, Mooney, Turbo Arrow (NA won't be much faster), Comanche, or Viking. A lot of fixed-gear guys will tell you that a retract is a money pit. That just isn't the case. Budget 2 AMUs a year extra and you'll probably come out ahead in the long run.
The second-most efficient path is a turbo, but only if you are willing and able to fly high. You mentioned a lot of local flights, and the turbo won't inherently help you there. You also mentioned issues with slow climbs, high DA, and cruising altitudes 10-11,000', and the turbo will help substantially for all of those situations.
I fly a Turbo Arrow III. I do a lot of long legs, and I don't mind sucking on O2 at 17,000'. I true out in the mid-160s at 65% and 12.5gph (ROP) in the mid-high teens. Going east, it is not uncommon for me to see ground speeds > 200 kts thanks to the strong tailwinds up high. As an added bonus, it is no man's land in the high teens. That's big for IFR flying. I get cleared direct pretty often at those altitudes. Going west, the headwinds can cancel out altitude efficiency, so the turbo doesn't benefit me as much. I still true out around 145 at 8,000, or 150 if I'm willing to go to 75% power.
I am not going to go so far as to recommend a Turbo Arrow to you. It happens to be the best fit for my personal mission x budget equation. I am not you. As with all planes in this market segment, the model has its fair share of warts and compromises. One lesser-known area that isn't a compromise is useful load. It is a sleeper hauler, on par with a 182. I have > 1000 lbs useful in mine.
Do look at Commander 114s. Vikings are not my jam, but with you being in a dry climate, they are an option as well - as long as you have a hangar. Comanches are not the easiest to keep maintained.
Also, every plane mentioned in this thread is an incremental upgrade. If you really want to make a big step up and can't stretch the budget any further, a partnership may be worth a look. You could surely find a like-minded partner in a big metro like PHX.