No estimations that I’m aware of. Just the pop reports and a good many on ebay.
If the projected production (not actual production) of Masaki promos was 25-39,000 based on a semi-official source, Grand party would probably be a bit less than that. If I were to guess maybe at or below 10,000.
The 2002 eCard lottery promos had a distribution of 5,000 each and the PSA pops are 80 for the least popular species and 165 for the most popular species (Charizard). That means about 2-3% of those cards have been graded.
Estimates for the Masaki promos were between 21-39,000 and the PSA pops for those are between 230 and 320. So like 1% of them have been graded.
So here’s a table for an estimated distribution of Grand Party based on the possible % of the cards that have been PSA graded.
If 1% have been graded - distribution about 50,000
If 2% have been graded - distribution about 25,000
If 3% have been graded - distribution about 16,500
If 4% have been graded - distribution about 12,500
If 5% have been graded - distribution about 10,000
Since the early years it’s always been seen as a valuable card (people used to think it was much rarer than it actually is because of the double star rarity). So probably a relatively higher % of them have been graded. But it’s really hard to give an exact estimate.
But I think 10,000-50,000 probably covers the realistic range.
I had factored the lottery promos also, and adjusted based on likely higher number Of grand party graded. It’s tough to gauge rarity vs scarcity based upon what’s available… As an anecdote, demand for the grand party had always exceeded the demand for Masaki, and far more again than the lottery campaign. When PSA 10 Lottery Charizard was $150, Grandparty was $200-250. I was probably too conservative at 10,000 though still, but maybe somewhere inside 10-30,000.