I'd be interested to learn what slugs (manufacturer, length, slug weight, and velocity) you had problems with as well as how they compare to the ammunition you've been able to shoot without issue over the past several years. Are they similar? If so- it does sound very likely that the most likely issue is that the spring in the tube magazine is weakening and screwing up the necessary dwell time. That "shouldn't" be an issue in regards to 'spring memory' with modern springs however not all springs/metallurgy is equal even amongst the same manufacturer depending on how it's tempered. If they aren't similar- then that's a different variable all together that was introduced and something else that could be discussed/explored.
Since you mentioned that it's the 'home defense' model- I'm making an assumption that you primarily shoot heavier loads through it and not trap loads but also assuming that as a 'home defense model' it could conversely be "over sprung" with a +10% spring (although I'd doubt this is the actual case) but if that's how Mossberg builds them, that could screw up the necessary dwell time as well.
As far as how to best go about troubleshooting it- I'll try to structure my response in regards to what's best for your wallet assuming my previous assumptions for your uses is accurate. The most expensive option would be to buy a bunch of other ammo keeping all parts the same with your shotgun and testing that. That'll tell you the most but would obviously be quite a drain on your pocketbook. Option #2, as Short-bus & cas6969 suggested, you might solve everything with a $20-30 gamble on a new spring. Stick with the original round wire design or go crazy and get a braided/flat wire "upgraded" design if that helps. You'll still need to invest a little bit more money on other slugs to test out the new spring but I'd imagine you'd be able to keep it under $100 all said and done between the spring/shells. That's probably the approach I would have taken for quite some time personally but the older I get, the more I watch my own wallet and time and that brings me to the third option- calling Mossberg and either have them screw around with it by sending it back to them (highest hassle factor but lowest cost) or maybe they'll offer to send you a replacement spring free of charge and in which case you're still in the hole for testing it with various shells but you saved the cost of the spring by making a several minute phone call.
If it's of any consolation- it's easy to get frustrated but these things happen with firearms. A relative of my picked up a similar semi-auto shotgun to your Mossberg, albeit in 20 gauge, from a friend of theirs and complained that it was jamming every 2-3 rounds of "high brass" hunting loads while chasing pheasants and we suspected a weak spring being the culprit. We went out to the range, were able to duplicate the issues but when we shot trap loads had the same problems as well that wasn't previously identified. We tore it down and the gun was filthy so we cleaned it up and brought it out a second time and still duplicated issues with both the trap & hunting loads but probably reduced them by (if I had to pick a random number) 60+% just by cleaning it thoroughly. We regrouped after the 2nd outing and bought another standard round spring (I think from Wolff but I imagine any reputable manufacturer would suffice) and low and behold on the 3rd outing and all subsequent hunting trips, with a little bit of time/patience/experimentation, the gun now runs as close to 100% as any other high quality shotgun with all of the low & high brass loads.
I submitted a similar post myself with trying to workout an issue with an M1 Garand I got from the CMP last year with ejecting the en bloc correctly and also decided to start with changing the main spring driving the action (although I haven't had a chance to test out whether that fixed things admittedly). So I "eat my own cooking" as they say in the South.
Anyway- hope that might be of some help to you, best of luck in getting it resolved.
-LD
