Of course you should pay extra for professionals who provide you with a valuable service. It has nothing to do with you having a VPS or not (unless you bought a VPS that includes a WP search service).
Relevanssi is not particularly well optimised for large databases. You can be as disappointed as you wish about that, but the fact remains that Relevanssi is designed for smaller sites. I'm not a professional; developing Relevanssi is not my job.
For high-level robust search that delivers fast results, you're simply going to have to fork out extra $$$, because developing something like that is difficult and requires lots of server power.
Also, Google custom search is available for free...