Advice needed: Webflow website with hosting held hostage by developers

Hi all,
I am new to Webflow (been building websites since 2001, have been on WordPress since 2011). I’ve customized and admin’d websites for awhile, though I’d never call myself a developer or designer. I’ve overseen many website projects, build-outs, and know how to design for UX.

Just started with a new company in Marketing, and they had engaged with a local agency to build their website long before my time - they were sold a Webflow website with site hosting.

The company’s relations with this agency has soured.

The site was paid upfront and the agency was supposed to maintain it and give us support for 1 year (until April 2021). Their response time has been getting progressively worse for the past 3 months, even for small requests - like to remove a checkbox from a popup form.

I have only been given design access, not admin access since the agency has built all their customers’ sites on their platform and will not allow me access to our own company’s site beyond basic design.

The company I am at wants to migrate the website to our own Webflow account so we no longer have to go through this agency and deal with the long response times and haphazard way they do things on our live site before confirming details.

The agency responded that the earliest they can do this is in 2.5 weeks, which is unacceptable to my company.

They wrote: “I’m happy to transfer the site and you guys can figure things out on your end, but if our time is needed that is the soonest we have available.” However they made it seem that we would absolutely need their time to transfer it.

In terms of the time they needed to spend, they wrote: “we will make sure all the custom code has transferred over, connect your hosting, test the forms, and test the connection with Memberstack for your investor portal”

I know very little about Webflow except for some basics. I don’t think they’ve even created a staging site for us - it’s just the one live site.

Can I simply have them transfer the project over to us - and hire someone else to “make sure all the custom code has transferred over, connect your hosting, test the forms, and test the connection with Memberstack for your investor portal” ???

Or is it most advisable for the same agency that created the whole thing - also transfer and test functionality - before we sever ties with them?

Please advise - there are a lot of unknowns here for us and company leadership doesn’t want to be delayed by this long timeline.

Thank you!
CJ