Hosting requirements for modified nop 3.6 site?

I have a modified nop site.
I purchased the nop license on 10/28/2015. Would it be version 3.5 or 3.6?
Sorry, modified so much that I no longer have the version number displayed.
Where do I look for that?

The bigger question:

The dedicated server I have it on goes down in 3 days.
Trying to move the site to somewhere low priced.

I have the rest of my sites running on a shared hosting setup that has .Net and SQL Server but I doubt they would let me register any special DLLs. I'm awaiting their tech support response.

Until then: any suggestions?

Thank you!

OK I found it is 3.60
And I found your page that recommends hosts.

One thing I'm still confused about is whether or HOW I can get a modified nopCommerce 3.6 site to run on a managed host.

AND my problem is that I need to get this site moved within 2 days and don't have much money to do it.
I've contacted Everleap and they seem amenable but can't guarantee the 2-day turnaround so I'm looking for other options. I know it is a lot to ask for.

Thanks for any ideas!