You should be able to use the line-out XLR (which I believe both versions that I've seen of the BA115 have) along with a 1/4" adapter if I'm not mistaken to take a feed from your Ampeg into the Marshall. It might be a good bit hot, so you may need to find a way to pad it back down to instrument level to work with the Marshall preamp... and you also won't be able to use the XLR then to provide a feed to the house board for live work, but IMO those would be the least of your concerns with that setup...
Again, just IMO of course, and I'm not sure what kind of a deal you've found on them, but you may be better served by taking the money that you have set aside for those Marshalls, and putting it towards some combination of upgraded bass rig and bass setup.
A decent quality bass cabinet should be more than capable of providing you with "clear sound with mid and highs and the thump of the lows" as you noted, across the entire range of your instrument - assuming it is set up well and the issue isn't with the bass itself. YMMV.
Just my 2c.