WordPress MU crashing server

Hi,
Interesting problem happening with our website, https://www.wa.uca.org.au. There’s an errant script running somewhere within our website that we can’t locate. Originally we were on a shared server, and it would occasionally crash the server. Over time however, it has built up and it began crashing regularly.
We were moved to a new server with only one other website on it (our hosting companies website). They moved their website off it, so our website is the only one there, but it is still crashing.

We’re now in the process of redeveloping, as it isn’t financially viable for our current site to remain there with the problems it has. However, we want to ensure that we don’t accidentally transfer over the problem to the new site.

One thought was because it is running on a sub-domain that is quite separate to our site, in that https://www.uca.org.au is hosted separately and controlled separately. Has anyone had a problem such as this, where there is an issue because of sub-domains and separate hosting?

Could it also be that we’re using WordPress MU, with folders for our congregations sub-sites (eg https://www.wa.uca.org.au/kalgoorlie/)?

Any advice on this issue would be greatly appreciated.

Ben