You can try sending all 6000+ to one of the current indexing services - most of the recent ones can index most urls I test with in 24/48 hours. However you're looking at prices between about $0.01 - $0.10 per url. Check out the services advertising on the BHW marketplace, try out their free tester credits and find one that works with your urls.
But I think a better way would be to identify your main hubs where the majority of these 6000+ pages are accessible from, and start backlinking them to shore them up and promote more spider visits. You of course also need to make sure that those 6000+ pages are index-worthy - 200+ words of unique text, internal links to other relevant pages, no 'noindex' tags or other bars to indexing etc