You'd need an oscilloscope not just a DMM.
Small voltage changes also aren't usually an issue to my knowledge and most things don't mind the frequency shifting either. I set my generator to do 62Hz at no load and I think it drops to 58Hz or 59Hz at full load. Really, 99% of things in my house wouldn't care if it's 40Hz or 80Hz, but some things apparently are picky.
I personally feel anything between 110 and 128 volts is fine, 130 is pushing it but I'd let it slide if it was unloaded. I think my older Coleman 4KW generator runs around 130 unloaded.
Allegedly the problems some digital circuits have are if the sinewave isn't a sinewave and how badly deformed it is, and you'll never see that with a DMM.
As far as THD and how good the sinewave is I'd truly be impressed if any portable generator, or even standby whole house generator could beat any power company. But who knows, highly inductive loads do weird things.
Voltage usually is not a problem, but frequency can be. I used to work for the Public Service Commission in the State of NY in the Electric, Water, and Gas division. We would get the very occasional complaint from a customer that something broke because of frequency issues.
We had a team from the Russian Electric Company (or whatever they call it) come in on some sort of international sharing of information. I got nominated to speak with them (through an interpreter). They asked about our policy for refunding equipment damaged by frequency changes, and I explained we did it on a sort of case by case basis, because they were so few. They were very confused and we had a lot of back and forth through the interpreter, before they made it clear that their grid would swing 10% in both directions on a given day, and they had a regular backlog of complaints. I explained that did not happen in, and they were kind of incredulous. It was actually a fun meeting, and I still have a glass dish they gave me as a thank you. They likely got it in the airport, but it is still a reminder of that meeting.
It's more on the local distribution level. This was 25 years ago, and maybe things are better now, but the interconnects for Ontario Hydro and Hydro Quebec were AC-DC-AC converted because they would pull the NY Grid at times. There was also a lot of discussion about who on the NYPP would be generating VARs. Granted the VAR are going to impact your power factor, not your phase per-se.When there's so many huge alternators running together I don't see how the frequency can shift much, everything needs to move together and that's a whole lot of "everything".
How much does the grid frequency actually shift? I've never measured anything other than 60Hz but my equipment probably isn't sensitive enough.
Glad to see you have it working! Just give give some thought to keeping the plugs dry when using the generator.