advice for warming up phono sound

Get a cork mat and recheck the alignment of the cartridge - particularly the SRA. Also check the tracking force. Give the stylus a good cleaning with a Magic Eraser (use it after every side!). Don't forget that LPs vary widely in SQ!

Almost forgot: get and use a record weight to get a better coupling of the record to the mat!

Thanks roberjerman, I will switch to the cork mat and get a magic eraser

Drop stylus into Magic Eraser. Do not drag it over tip.

the harshness is likely coming from your phono pre.
if you are a DIYer you can replace those red wima caps with Nichicon XY series, much better sounding cap.

If not a DIYer, then would suggest looking for a diff phono pre.

Tubes will help.
But setup it pretty important.

The Oracle mat is far more neutral than cork. What is important about the mat is that it should absorb vibration in the vinyl that results from the stylus tracking the groove. Turn the volume all the way down and play an LP- the more sound you can hear coming from the stylus itself, the less the mat is doing its job.

Arm height is important also. This is one way you adjust the rake angle of the stylus, which should be at the same angle as the cutter stylus was when it made the groove. This is about 92 degrees (but not exactly as the actual cutter angle varies from LP to LP as not all cutter styli are identical).
Some cartridges have the needle slightly off on the cantilever, making the correct rake angle difficult or impossible to achieve. This will result in sibilance and the like. So its a good idea to find out if your cartridge is alright first.
Many preamps are sensitive to RFI and ultrasonic noise, and this is generated by the cartridge when it plays. If your preamp has this problem, it may sound bright and the cure is loading the cartridge (so the loading is for the benefit of the unstable phono circuit, not the cartridge). The thing is, loading the cartridge causes it to be less compliant, so its to your advantage to work with a phono section for which loading is unimportant.

Thanks atmasphere,

Yeah I think I'm going to have to address the arm height issue.  Unfortunately, the Rega P3 doesn't have arm height adjustment.  Looking at the angle of the arm while playing a record, it looks to be right at 90 or maybe a bit under.  It looks like I'll have to get some shims to raise the arm a little