I guess that depends on what the real influence of this decision is.
You could do that but "kit" designs are probably not where you are going to find this solution. The crossover is the easiest or correct way to fix this issue.
However I do find it appalling that the actual bass response of the speakers is that bloated? Were we able to confirm this?
If you cannot or do not want to change placement, I will still recommend that you add in a notch filter or one of the other suggestions I posed to actually correct this issue even if you upgrade your speakers.
It would be interesting to note the actual amount of room gain at this frequency range. Especially considering that your current crossover will have response down by -12db at 40hz. If you have a peak of +12 or more right now with the x-over engaged (assuming your current speaker's bass is not bloated), even with a different speaker you could still have issues.