How to reproduce the Gaussian 09 SDD basis set in Gamess-US?
SDD is a basis set description, which uses Stuttgart/Dresden ECPs. They are readily available for download at the BSE, but also via Univ. Köln. And they are pretty easy to pick out. See the Pseudo keyword for what is Gaussian 16 is using currently, which should be the same for 09. At least in the BSE there hasn't been an update to the S/D ECPs since their initial upload. See the related notes included at BSE and pick the appropriate size. The more problematic part is finding the BS for the orbitals that are actually described. I believe this is the correct choice, i.e. Stuttgart 1997 RSC. Please review the literature specified on the Gaussian homepage about the implementation of SDD (should be about 20 to 30 papers), and then you can cross-reference them to the references saved in the BSE library.

The work is from the earlier days of computational chemistry, so it is quite fragmented. I believe the ECPs are still popular and used in the correlation consistent Dunning basis sets. The orbital parts I wouldn't be too sure about. There are plenty of other choices out there and it would be wise to review the literature to see what is the state of the art for strontium.

Why not use the move away from Gaussian also as a move to a less fragmented, different level of theory? If you want to compare the data to previous calculations, you have to recalculate them anyway, why not choose a method which is a bit more consistent than the SDD basis. And depending on what you are calculating, you might also want to look at different software suits, e.g. Orca, Psi 4, Turbomole. Gamess certainly has its strengths, basis set implementation and handling is unfortunately not among those.