Options to fix a loose post and core (via a tooth root fracture) for my 3-tooth, supported fixed bridge?

Your options are limited in this case.  The post and core is hopeless if there is a root fracture and extending the bridge places too much force on the adjacent teeth.  By far the best option is dental implants.  This will help in preserving as much bone as possible.  Though costly, it is the most sound treatment and there are options such as Care Credit that will allow you to pay the treatment out over longer periods of time.  Good luck.  

You have a very difficult problem.  Depending on the location of the fracture it may  not be restorable.  It is possible to extract the tooth and do a longer span bridge.  The best solution long term solution may be an implant  or two implants even though your insurance doesn't cover implants.An older technique can sometimes be used to salvage your existing bridge and the fractured root.  A telescopic post and crown can be made to fit the tooth and the inside of the bridge.  I have done this many times over the years, not always possible but frequently a viable option.As to putting in larger post.... probably increase risk of future root fracture.  

If the root is fractured, and is a single rooted tooth, then there is little hope that the tooth is salvageable and extraction would thereby be indicated.Yes, rarely does insurance cover dental implants, and even if it did, it would only give you partial coverage of what the total amount will be.Yes, four unit fixed bridge or two dental implants (saving the one tooth crown by "sectioning it" from the rest of the 3-unit bridge) are your best choices.  If either of these two options are beyond your budget, then extraction and a removable partial denture or a "flipper" (very economic but not a long term solution) are you remaining choices.