Yes, you have a real problem here!
I know I am probably telling you things you already know, but for completeness let's start from the beginning. You have five tuners and you are looking at all three satellites (because you have HD) so you need five outputs from the dish. No getting around it. That means a 4x8 multiswitch, taking the four outputs from the built-in multiswitch and giving you 8 outputs.. The new 4x8 (most are 5x8 so they can diplex an OTA signal onto the same outputs, but let's talk about that later) could in theory be at the dish or in the house. A lot depends on the length of your cable runs - using an unpowered multiswitch might allow you to have the switch at the dish but may not work because of your cable length. If you have to use a powered multiswitch then putting it at the dish would require power there.
Once you have solved the multiswitch problem then we come back to the "only three cables" issue. I can't tell from your post whether the problem is getting four cables to the house or getting a fourth cable through the house exterior/interior walls to the room where the TiVos are. Just for the moment I will assume that you can get four cables to the house somewhere and put the 4x8 multiswitch there. You will have to run the cable for your fifth receiver from this multiswitch (instead of from the dish) to the remote receiver. This leave you with four cables to get to the two TiVos. Two of the cables will go to your HD box leaving two outputs for the other TiVo. It is possible to "piggyback" the two outputs onto a single cable using devices called stackers/destackers. Not cheap but possible. I have not used these myself so you will have to do more research on suitable devices.

I did see a special 3lnb replacement dish with built-in stackers (TSAT242) which allows you to connect the dish with just two cables without the need for multiswitches. At the house you then need a stacker router which seems to be a combination destacker and multiswitch - some of the outputs are already destacked and some are left stacked - you would use one of these stacked outputs routed over a single cable to your standard TiVo and then have a destacker at the TiVo. This would mean: only two cables from the dish to the house, and only three cables into your equipment room. Still need the fifth cable to be rerun so it goes to the stacker router. Probably cost about $1200 in total. Go look at
[Link: 9thtee.com]

A word of warning. DirecTV is in the process of adding new satellites and moving to MPEG-4 compression and away from the existing MPEG-2. All new HD channels, including local channels over HD, will be on MPEG-4. This will require a new dish and new receivers. At present DirecTV is rolling out MPEG-4 HD locals in a few major markets and will move to cover most of the largest markets during 2006. The conversion will apparently be "free" (some people are reporting installation charges of up to $99). There will be a new DirecTV HD PVR (not TiVo) some time in late 2006. These new dishes and receivers will almost certainly not work with the stacker/destacker solutions currently available.. No doubt someone will develop stacker/destacker technology that works with the new dishes but I haven't seen anything yet.
If I were you I would bite the bullet, run a fourth cable to the house to connect to a 4x8 powered multiswitch, reroute the fifth cable and somehow get another cable to the TiVo room. Then you might be able to get the installation upgraded to the new technology (replace dish, receivers and multiswitch through the DirecTV upgrade program) free or at low cost, if the installation is in one of the areas that DirecTV is upgrading). Any other solution is messy, expensive and short-term.

Hope this helps....