Could I find a Rod that does all of these well? I'm looking to stay below 225$

What weight range are you talking about with these lures?  Is there a length preference? I'm asking because for topwaters I prefer a shorter rod than I do for traps, and for square bills I can use either a longer rod or a shorter rod but it depends on what the size of the baits I'm throwing. Now, not knowing any of the variables mentioned above, there is a rod I think will work well for all and it will only set you back $75+ shipping costs. Over at FFO, there is a Fenwick Elite Tech Smallmouth 6'10" MH-MF casting rod, I already have one, that rod isn't soft or parabolic in action. What you get is a stout rod that flexes further down the blank to help keeping the fish pinned with trebles without being parabolic. That rod will work with square bills 3/8oz and up, it will work for the same size traps and top waters as well as it is rated 3/8oz to 1oz. There are rods that will work better for one technique or another but for a rod that can do them all and do them well at your price level, the ET Smallmouth 6'10" MH-MF is the rod for you.

Dobyns fury or champ 705cb.  

Lew's custom speed stick wart special or trap caster.

Abu Ike delay series 

so many options in that price range that you literally have about 100 option lol

https://www.*.com/G-Loomis-IMX-MBR-Rods-p/g-loomis-imxmbr.htm

What about the 843C mbr? Sign up for the mailing list and save another $25. Puts the cost under $200.

I need to stop knowing about these deals it makes me want to buy more rods