New Subwoofer vs Bass traps.

I have a budget Infinity subwoofer and I used to use it with a pair of monitors that crossed over at about 60hz and I set the crossover on the sub to about 50hz(the lowest setting). This worked fine. Now I have some floorstanding speakers that go down to 35hz and frequencies are overlapping and causing lots of boom. Which would be better, replacing my subwoofer with one that will cross below 35hz to avoid overlap or could I get a bass trap to control the extra boom?
I would not advise using a bass trap for this. For one, it's unlikely it will do what you want it to do in terms of attenuation. Bass traps work for broadband applications, with some exceptions such as capacitive style bass traps. The capicitive style could work, but it's very dependent on speaker placement and could thus lead to some other problems/issues. If bass was good before you changed speakers, I would opt for the second route and get a speaker that can properly cross over for your new speakers.

The crossover at 50hz is way too high for your new speakers. Are you shure you really need a sub now? If so, you will need one with a flexible and low crossover point. I have a REL Stadium III which I crossover at 34hz and my mains only go to 50hz +(-) 3db. Higher settings produced too much bass at certain room boundries. Just my two cents.