Would increasing the gain in the amp give more weight to the sound? Any negatives?

Inserting transformer? Interesting idea.
As I wrote in another thread, I currently use tape deck monitor as a kind of active preamp and run phono through the deck. This gives me just the right amount of what I am looking for with a slight loss of resolution. Pretty good but certainly can be improved.

The phono stage is AcousTech and the amp is Redgum RGi120, both SS.

well musical fidelity has inexpensive unity gain buffer device that also inverts the phase. one can be placed between the source and amp, but active preamp will work much more efficient than even mentioned inverting transformer. I struggled when I had Creek 5350 SE integrated amp till I purchased active preamp Classe 30. This preamp turned polite and shy Brittish amp into substantially better version...

Hi inna,
Your Redgum is a very low 10kohm input impedance, which could trouble some sources that have high’ish output impedances (eg >1kohm) this could be your problem if you phono stage is >1kohm.

I can’t find what the output impedance is of your Phono stage is, but I did find out just one of the few AcousTech phono stages, was designed by Ron Sutherland .

I just found this if it's your model.
"AcousTech Electronics PH-1 phono preamplifier "
" Recommended load: 10k ohms or greater"

You are right on the min, with the 10kohm of the Redgum if this is your Phono stage.

Cheers George