Bank of Cyprus will not see any problems of incoming transfer from SVG company if it is for use or software, not a comission for unregulated financial services.
If you need SEPA and SWIFT bank accounts, not EMI accounts, you have to talk to european banks.
The best way to have account is not to have a bank account of SVG company, but use so called payment agent. It will be a company which will be fully owned by SVG company and will handle payments as so called payment agent.
There are 2 countries, where a payment agent company does not need a financial license, if this company provides services just for other company which has to be a full owner of payment agent.
Banks are willing to open bank accounts for this payment agent companies. So, you will have a structure, where SVG company will be a 100 % owner of other european company and this european company will have a bank accounts in more banks and will handle apop incoming and outgoing payment in a name of SVG company on its bank accounts.
There is no way how you can have SEPA + SWIFT bank account for unregulated company from SVG in any reasonable bank. You have o use this bypass.
Answers to your questions:
1. Is there anything we could do so we can find more banks and PSPs?
No for SVG company. But you can create your own payment agent company and it can be much easier to have a bank account for this company.
2. Is there anything we could do with the Cyprus companies that could help us somehow? any restructuring or something?
No. Not needed.
3. Any legit crypto exchange that we can send crypto and exchange to fiat and withdraw to our bank account of SVG company?
No. But if you will have a payment agent company, banks will gladly accept incoming payments from Kraken and AdvCash.
4. Will we need the bank to be crypto-friendly if we want to transfer fiat from the crypto exchange?
No for FIAt to Crypto but yes for Crypto to Fiat.
I see, here are few members who are offering their services..
So just a short reaction on them: You do not need to be regulated if you are not doing a business with investors in EU nor USA, Canada.