We can't see tension via the internet, so you have to trust our own, and the mechanic's judgement on that score. OTOH- though I'm not a tighter is better man, I do raise tensions when I'm using fewer spokes

As for the squirreliness, was it always this way? or is this a new thing? The reason is that wheel rigidity depends on the amount of steel; more or thicker spokes make a more rigid wheel, so a 28s wheel may be a bit flexible for a heavy rider.

Also check for a tire that runs true. Often I'll ride my commuter and it's feel like the wheel is flexing, loose or wobbly. I'll stop to check spokes and all would be OK, later on, I'll find a cut sidewall and a tire with something of an S-curve, which makes the odd handling.

All I can say at this remove is that you have to be a detective and see if you can sort out what's different then before when it rode OK.