Does anyone know if it's possible to transfer a LP site while it's suspended?

I need to move my site to a new host, but my account is suspended and I don't know how to do a transfer without ftp access.

I upgraded Wordpress on my site a week or so ago and apparently the cache function didn't get reactivated properly.  Which resulted in a new php-cgi process getting triggered every time a page request was made.  This in turn seems to have caused the site to exceed its CPU limits - which I wasn't aware of because I don't know of any way to monitor that.  So my account got suspended last week.  I responded to the suspension notification the day after I got it saying I wanted to fix the problem, but was going to be out of town on Wednesday and Thursday, so I wouldn't be able to do it until I got back.  Unfortunately, the support staff went ahead and opened up access to the account on Wednesday and then suspended it again on Thursday.  So when I got back on Friday, I wasn't able to get to the wp-admin panel.  I replied to the suspension support ticket, asking for the site to be opened up so I could get to the wp-admin panel, put the site in maintenance mode to avoid resource demands, and install the wp-supercache plugin to fix the problem.  In response, the support staff has told me the site cannot be reopened until I make satisfactory script changes through c-panel.  Since I don't know how to do a server side installation and/or activation of a plugin, I'm pretty much permanently shut down.

So, even though my LP account is paid up through the end of this year, I'm thinking I need to move the site to a more user-friendly host.  But the account suspension also has cut-off my ftp access, so I can't download my most recent backup file and I don't think a new host can get in to do a direct transfer.  Does anyone know if there's a way around this problem?

Thanks

Yes, I told them in my ticket response Tuesday night that I was going to be out of town until Friday.  When I got back on Friday, I found responses on the ticket telling me the site had been opened up on Wednesday but then closed again on Thursday.

 I replied to these messages Friday morning, pointing out that I had said I would be unable to do anything on Wednesday but also apologizing for not having been there and politely asking for the site to be opened so I could do the plug-in fix through wp-admin.  I got a response later on Friday saying it could not be reopened and I would have to correct the problem by making changes to "the files and the databases" though c-panel.  I replied Friday night saying I don't know how to make the right changes through c-panel but outlining the specific steps I would take through wp-admin to install the plug-in that the support staff had recommended to fix the problem.  Again, I did so very politely and told them "I'm begging for a chance to fix this through WP Admin." 

Twenty-six hours later, I got a response from a JSA saying that because "this issue is reoccurring with your account, we will not be able to resume the services of your account."  (Of course the reason the problem had reoccurred was because they opened up the account on the day I had told them I'd be out of town.)  Instead, they told me I should "make appropriate optimizations via c-panel" and then provide them with the "details of the modifications done" so they could decide whether to reopen the account.

If I knew how to do the changes in Wordpress through c-panel, I would.  But I don't know how, and the support staff doesn't seem inclined to give me any advice on how to make the "appropriate optimizations" from there.  So I just want out, and I don't even care about whether I get a refund of my remaining 6 months of service.  Except I can't even do that since my files, databases, and backups are being held hostage by the ftp suepension.  I replied on my support ticket about 8 hours ago asking them to at least allow me ftp access, but haven't gotten any response to that.

I'm worried though, that since they won't give me wp-admin access they probably won't give me ftp access either.  But I'm wondering if there's a way they could allow a new host to do some sort of direct transfer.  Does anyone have any experience with whether or not something like that can be done?

Hi EvanH. What is your ticket number for this? Be glad to check into it.