What DNS servers does your DHCP scope give out? That should give you some clues as to where to look. If your PC is given an external DNS address, then you're out of luck, but if it's an internal address then whatever has that address may have the capability to hold custom records.
And if it doesn't, maybe it's time to set up your own DNS server so that you can do stuff like this. It's a fairly simple process (says the network engineer who's never done it before). If you're running an Active Directory domain then you should be able to add the DNS Server role to your domain controller, or look at BIND ifyou're a Linuxy person. And if you've got a domain controller, you could also add the DHCP server role to it, and control things yourself that way, without having to fight with a shit router.
I would say leave the managed switch to do switchy things, though. Let it worry about moving packets around and very little else. It's not a normal place for a DNS server or a DHCP server.
Configuring a router for ADSL shouldn't really be that much of a big thing (the ISP should be able to help, especially if you're paying business rates), but I'd also say that you should maybe have a look at the local IT firms and ask them how much it would cost. They do that kind of thing all the time and chances are it'll come in cheaper than paying you to spend much longer working it out, and if not cheaper then at least you'll come out of it with a simpler setup. If you find the right firm, they should be able to set it up for you and provide proper instructions on how to make the simpler changes without having to go back to them.
I've got a few things to try without messing around with DHCP or DNS. The server has to stay up and WAN-accessible 24/7. I've added a virtualhost on a port not open to the WAN, and doesn't have the redirect (which fortunately isn't in htaccess). Not able to really test any LAN stuff until I'm back in the office tomorrow. I have until the 'old' network cuts out (in a coupla weeks iirc) to sort this out as best I can. We'll see how it goes ...
The thing is, though, that you talk about "messing around with DHCP or DNS" when DNS is the exact tool you need to do what you need to do: have an external URL resolve to an internal IP address for devices on the LAN.
Talking about doing stuff with htaccess, redirects and virtualhosts sounds like the kind of fix that gets put in because it seemed sensible at the time, but ends up being a millstone round your or somebody elses neck for the next few years. It'll just be that thing that somebody put in in the past, but nobody ever has the time or inclination to take it apart and redo it properly.
Setting up an internal DNS server wouldn't have any effect on the accessibility of the web server from the internet (because your port-forwarding is already being done by IP address), but it would give you the simplest, most understandable way of accessing the server inside the LAN.
Basically, and I'm not trying to be nasty, because I know the kind of pressure that gets put on technical people in small companies, but you're bodging a fix rather than spending a little more time on it and getting a much better and more capable solution.