I started really looking at the P7 and I can see why Erik continues to recommend this time after time in multiple threads -- as a good priced preamp. In this budget area, I would choose the P7 over the P5 or 2100 every time, even though you don’t need 7 channels!
P7 has an extremely good linear power supply architecture (which is core to sound quality in my opinion). It uses resistor ladder circuits for volume control.
P5 and the 2100 looks to have switching power supply and uses a carbon film or plastic film potentiometer for volume control. Local power supply filtering for analog circuits is also not as good as P7.
The Class CP-800 is going to be a much better preamp than P7, but significantly more expensive too. Both the P7 and CP-800 are towards the high resolution transparent character, so they would not be "softening" your sound.
If you want a softening effect, McIntosh is the way to go. The NAD c165Bee might also be a good option as I have read NAD tends to be on the slightly warm side.
Be careful with tube preamps as tube devices could easily go into a way different sonic signature, such as being chimey or lush or bloomy. This is an entirely new area of personal preference where I don’t have any experience, so I cannot comment.
What is your source/DAC? Are you listening to vinyl or CD? Sometimes a soft/messy preamp can seem to sound harsh, where a very clean/transparent preamp can improve overall clarity and remove harshness. An inadequate power supply in preamp can also cause it to sound shouty and harsh. It also depends on system synergy and can be influenced by other things such as interconnects and speaker cables.