Wow, Steve, sounds like you are getting a lot of great answers.
To choose between lemon neoclassic and lemon mousseline:
-NCBC is richer, denser, more deeply yellow (which is nice against a white cake) and less work/easier.
-MBC is lighter/more airy, harder to make, more time consuming (because of making the curd first) and requires fortitude to see it through any curdling. If you love lemon curd, though, you will swoon over this.
For cooling whipped eggs/whites:
I know of two tricks here, first, keep a a couple of tablespoons of butter at 40F and add it one at a time to the somewhat cooled eggs (maybe 80-85 F) to cool them down the rest of the way.
Or, after several minutes in the mixer, cool with water bath. Either get a water bath attachment for your mixer or use a wet towel around the outside or place the bowl over another bowl of cool water and whisk. In an ideal world the eggs and butter should be close to the same temp and not too hot or cold, say between 65-70.
For Mousseline, butter at 65 F is best. If (or maybe I should say when) it curdles, check the temp to make sure it is around 65-67. Use water bath if necessary, and beat until it comes together. Continue to add the rest of the butter by the tablespoonful.
If your buttercream tastes too buttery and you’re using unsalted, add more flavoring. Most of Rose’s buttercreams will hold a little more flavoring (puree, liqueur, etc) than called for, but then you have to be careful about stability, ie, don’t leave the cake out for a half day.
Good luck, and we’d all love to see pics!