About many inches is the old insulation below the top of the joists?

If you can add a 3.5" unfaced bat on top of the old bat without compressing it, do that before putting the next layer perpendicular. An air pocket isn't awful, provided there are no leaks, but that is almost impossible to achieve.

mike_home, the gap varies but ranges from 2-4 inches.

My thinking is a 2-4 inch air gap is going to allow a lot of cold and hot air to bypass the added layer of insulation. The R value is not going to be as high as what is listed on the insulation material. I think you are better off laying the new batts parallel to the old ones.

I would start with something like R-19 3" unfaced rolls on top of the existing to fill in the voids. Then I would use something like R-25 bats perpendicular.

Yes go parallel with existing insulation to fill the joist spaces, then perpendicular on top of that.

Thanks, everyone, for your advice. I ended up using R-15 3.5" unfaced batts, placed on top of and parallel to the existing stuff, which brought the insulation up above the joists. I then laid out R-30 9" unfaced rolls perpendicular to the joists. I think it turned out ok. Certainly one of the more annoying jobs I've done, but I think I've done myself a favor in the long run. Thanks again for your help!!

I was going to suggest this but did not since it is a lot of work. Glad to hear it worked out for you.

For sure not fun, one of the few jobs better done in winter lol.

Do an internet search on Air Sealing first before you add the insulation. At that point, you can just loose fill blow over the top.