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I haven't had any orgasm since Jan 31 and for several days now I'm desperately horny like hell too and want to cum so badly it's driving me to more intense sexual frustration than I thought possible. All I can think about is an orgasm. 23 days without ejaculating feels like my absolute limit. I had only agreed to 20 days, but then rolled the chastity bingo, which says my next chance to cum isn't for 18 more days! And even then no guarantee. omg I can't wait 1 more day, let alone 19 or more. Please let me cum...I really NEED to cum. I've never been this desperate to cum. Should I go ahead and start edging for what I'm certain will be an explosive, extremely pent-up multi-spurting orgasm? When/how will I actually get to cum?

I'd say an orgasm should be really enjoyable as a compliment for your effort and what you'v done, and to stimulate you to do it again.
You'v done so well, and if you are completely certain to cum, then listen to my suggestion. If you think you can hold one more day, or even one more hour - do so. Then when your dedication to cum becomes absolute, read my suggestion:

Spoiler: show

I would suggest you picking a long sexy video, maybe from your "The best of all times" collection... and masturbate slowly. Don't rush. Observe the sexy images before you.
Then start edging. And no matter how much you want to cum, try to hold off as much edges as possible. "Just one more. 1 edge is so simple, after all. It's a matter of personal pride. It feels nice and it builds you up to what you KNOW would be sooo good of an orgasm". If you start cumming, you can either ruin it, if you think you can edge a little longer, or stroke to full orgasm. No pressure, it's your lucky time, it exists for your pleasure, and nothing else. You don't need to hurt yourself with frustration more, than you deserve now.
Then, when you are completely satisfied with yourself, wait for the hottest possible moment, while staying close, but not edging. And cum. Enjoy it throughly. Don't stop your hand, stroke your cock slowly all the way through orgasm to get the best of it.
When you are done, I suggest you wait a minute or two for refractory period, while watching your favorite model being licked and fucked, and immediately stroke yourself to orgasm again, with no edging now, just a pleasurable ride!

Enjoy, if you pick this option.

I always joke around
and say christmas is a perfect time to wait for
since you asked when,,,

The ultimate denial is to wait for a wet dream...then be denied because you already had your relief!

Thanks for all the guidance. Somehow I made it through the night without cumming, so now up to 24 days without ejaculating and the urge is amazingly even more intense than it was yesterday. Each day I feel like I can't hold off orgasm any longer, but today feels like the real deal--I MUST cum somehow asap.

As others have said, take it one step at a time. Don't even think about 18 days, just take it a day, an hour or even just an edge at a time. Everyone has the willpower, you just need to unlock yours.

Thank you everyone for your replies, guidance and feedback. I was extremely tempted to just go ahead and ejac last night. INSTEAD, I was able to get to the edge 3 times last night simply by setting a vibrator atop my zipper. But after that the risk of going over the edge and involuntarily ejaculating seemed too great. It seemed to help provide a slight bit of "relief" in some small way, albeit for only an hour or so. (Usually I have excellent control of being able to STOP my hand or other activity before any danger of cumming even after hours of edging and days of orgasm denial.) This time, 25 days' worth of pent up cum is really making my testicles feel huge. I so NEED to cum I want to shout! I'd have thought the overwhelming urge to spurt might have gone down a bit by now, rather than intensifying each day. Every night I feel like I can't hold back all the pent up cum any more.

So...have you managed to resist the temptation and hold out?