How serious are these numbers?

[factor]

Snore, sure -- but my wife retrained me early on and it's minimal.

Any is not normal.  I think retraining means she learned to put up with it..  You most likely have had OSA since you started snoring.  Ask your wife what year that was.  In general that is how long you had sleep apnea.
Read My Story below in my signature.  

is this as serious as they told me it is?

Yes, Any AHI above 5 is sleep apnea.   Your numbers are severe at 36.  You need CPAP as soon as you can commit your mind to it.  As others have said it most likely helped bring on the Afib. 

are these numbers not to be ignored at all and just a strong indication that I have really no other choices?

Ignored them for to long already..

So I don't expect sleep doctor expertise here (I guess)

expect better.  We will actually help you and not send you a bill...

how often should I be retested? 

Unless something requires it you wont need it.  You have it and it is a lifetime thing like HTN or afib.  

Has anyone ever gotten into CPAP stuff and then improved to the point where they don't need it again?

Very few.

There a tendency for it to make you more dependent on it?

More than every time you sleep? no not really.

The biggest problem I have (besides the usual discomfort of trying to sleep with a face-hugger on me) is that I hate the idea of adding more permanent tech to clutter up my health regime and... well, life. I mean, both of us just retired, we were hoping to travel a lot more.

You adapt.  Its your life and health.  It wont stop you from traveling.  I makes you a better healthier person.

FTR, I'm very fit, and thin.

Its not only a fat mans illness.  That is why it gets some people that are Thin "healthy"  and they think all is well. 

My wife is all for going ahead with CPAP

Listen to your wife..  She loves you and is smart.  Its going to help her to...   (read my story)

We all will be here to help you all along the way.  So like Nike "just do it". Ask for a ResMed device...

[Sleeprider]

If you want to minimize the feeling of a mask on your face, use a nasal pillows mask like the Resmed Airfit P10. The smallest lightest interface on the market today, it is also very quiet and will not blow air on you. You can skip the titration and just get a script for the Resmed Airsense 10 Autoset CPAP. This device will quickly help you to zero-in on an effective pressure range, and because its "exhale pressure relief" (EPR) works like bilevel up to 3-cm of pressure, it will let you address any flow limitation or hypopnea that you have. It is a full data machine and with OSCAR software, you can document your progress, optimize and provide feedback to your doctor. A titration test is just another night in the lab, and is rarely helpful.

[hegel]

I agree with the others: your numbers are seriously bad. You need cpap for sure. Here's the thing: you will feel much better when you use it.

Will you get better on your own? No. emphatically, no.

Apparently you can rent a machine from Aoria if you want to just try this. Better to buy a Resmed airsense 10 auto and cut to the chase.

I also think starting with the P10 nasal pillow mask is a good idea.

There is a bit of a learning curve but if you do it right, you'll likely feel the benefits very soon. You may not even realize what feeling well slept feels like anymore because your normal way is to be sleep deprived.

I'm with Kaiser and they sold me a machine at a huge discount and provide different style masks to try to find one that's most appropriate. Your wife will be very happy, especially if like me you lose the sleep deprived grumpiness and gloom and become more energetic.