Is the cartridge loading the same for both the new and old phono stage/section? That warm and "wet blanket" sound can be the product of incorrect loading. If you have options, try a different setting for loading. The right value for loading is somewhat dependent on the phono stage, so the optimal value may differ for the two stages so try all options available to you.
Yes, tube choice can make a difference. You mentioned the options you are considering, but, you did not mention what tube brands/types you started with that you don't like. This information will help others in offering suggestions on which way to go.
If you are looking for a clear, somewhat lean sound with a lot of "jump." I would suggest Telefunken, but some of those choices can be quite pricey.