Disclaimer ... I'm not a gunsmith (or a polymer chemist), and whatever you do is at your own risk. All I can offer is some general guidelines, based on what I've learned about plastics over the years, and a suggestion for a possible approach. Your best bet would be to start by consulting a gunsmith.
First, the bad news ...
The polymer lower is a thermosetting plastic, which means it can't be melted (welded) back together. If it were (as would be true of a thermoplastic material), the lower might fail (melt) under the heat of intense firing. Heating a thermoset will not do much of anything, until the temperature gets high enough to destroy the polymer. Nor is this the kind of plastic that can be solvent welded. The material used for the lower was chosen to be very inert to all kinds of chemicals, else it'd be vulnerable to cleaning solvents.
The only alternative would be an adhesive, but I worry about anything commercially available being strong enough to withstand the stress of firing the rifle.
None of the epoxies or "plastic welders" (such as methacrylate-type adhesives) are liquid enough to seep into the cracks you mention. They need to be applied to the mating surfaces of (separate) broken parts. Super glue might seep in, but it's major weakness is not being able to withstand shock loads (ie, firing).
Finally, it's more than likely that the plastic of the lower is "filled" with something like glass fibers. These fibers produce added strength. All the fibers originally running across a crack are now broken, so an adhesive repair of the crack will be weaker than the original.
That said, you or your gunsmith don't have much to lose by trying to make whatever repairs you can. A suggested approach: fully break out the cracked pieces, apply something like JB Weld to the "mating" surfaces, then drill the excess JB out of the hole once it's well set. But don't be too surprised if the repair fails.
PS - Just out of curiosity, is this the Bushmaster "Carbon 15"?
