Julie,
I too, feel the same and offer the same heartfelt wishes that Cookey has expressed.

This is still very serious but, not as bad as the carotid scenario but still very serious.

May i offer some potentially helpful advice.

You will not be able to, and Rich will not allow you to put a dark towel in his mouth to his advantage.
Got to your pharmacy and buy some 2x2 sterile gauze. Buy about 500 they are very inexpensive. Call your family dentist and ask if they have or can provide you with "Surgicell". This is a hemostatic impregnated gauze, if you cannot get it send me your address and I will send some to you.

If my family member was in Rich's position and the worst happened this is what I would do. (Cookey chime in anytime if you can offer anything, I'm shooting in the dark here.)

Julie, I personally do many biopsies in my office, remove imacted wisdom teeth, place implants and do gum and bone grafts. I have run into a few bleeders in the past. Some were the result of surgery and others medication. If I had a lingual artery bleeder that I could not ligate, this is what I would do until paramedics arrived.
The vessel you are describing is the lingual artery. It has two branches, one on either side of the tongue. The following will only work if the rupture is reachable with your fingers.

1. Call 911 tell them what is going on, ask them to meet you en-route to the hospital tell them where you propose to meet. If they will not do this stay put until they arrive. Then Rich will need, immediate direct bi-manual pressure. If you place your index finger behind the perforation/bleed and your thumb outside the mouth under the chin and push them together they will almost touch each other with tissue in between. ( try this for yourself to see what you need to do.) Rich can do this himself while you grab the gauze and surgicell.

2. Take 1 surgicell gauze and fold it in quarters, take 2, 2x2 gauze and put them on top of the surgicell. Place them over the bleed under the tongue, surgicell side down, reposition Rich's fingers on top of the gauze behind the bleed, squeeze finger and thumb together again. Use two fingers if you can.

3. Keep his head above his heart and meet the paramedics or wait until they arrive at your location. Use as much gauze on top of the surgicell with as much pressure as can be placed.

Carry the gauze and surgicell with you everywhere. This may be helpful, and may prevent the worst. It is by no means a tried and tested procedure. It is what I would do under the circumstances.

My prayers are for Rich and you,

Mike