You're correct, in your circumstances it wouldn't be legal to bring an AR into Mass.
An AR is a "large capacity weapon" under Mass. law, so you would need a Mass. non-resident LTC to possess one in MA. Some people here on NES disagree with me on the subject, so I'm posting a link below where you can see both sides of the argument.
http://www.northeastshooters.com/vb...-into-MA-or-CT-for-Competitive-Shooting-Match
Violation of that law is a felony.
Handguns are a different matter. There are only two ways that you can legally bring handguns into Mass. as a non-resident; either by getting a non-res. LTC, or as a non-resident hunter (with a hunting license), a competition handgun shooter or collector attending an exhibition. That exemption also only applies if you have an LTC issued by a state who doesn't issue LTC's to people with felony or drug convictions (resident or non-resident permits from Connecticut, Pennsylvania, and the US Virgin Islands all meet this criteria).
In other words, you can't just bring handguns into Mass. for target shooting unless you have a non-resident LTC.
There's another problem. In order to get a Mass. non-resident LTC, you must have an LTC issued by the state that you live in.
http://www.mass.gov/Eeops/docs/chsb/firearms/MIRCS Non-Resident LTC application - for website.pdf
From what I understand RI can be unpleasant about issuing LTC's, so that might trip you up.
There's another issue here as well. Even if you're bringing in handguns under the hunting/competing/collecting exemption found in MGL 140-131G, they still can't be "large capacity firearms." You said you have a Glock and a Sig. The only Glocks that aren't "large capacity firearms" are the 36 (compact slim .45 ACP) and the 37/38/39 (.45 GAP models). The Sig P225, P220 and P239 aren't considered "large capacity firearms" either, and there might be more but I'm not a Sig guy so there may be more models that I'm missing.
Basically you'd need to tell us what model handguns you have to know if they would be legal in some circumstances, but again, even if they were legal to bring in under the competition/hunting/collecting exemption, it would
not be legal for you to bring them to Mass. for target practice.