Totally feel your pain...been down that road all too recently...
We also had to replace a full-size violin in haste (teacher declared it unplayable for other reasons) and haste really is pressure you don't need, especially with a young teenager who will be hesitating between pursuing his ideal sound and not putting too much pressure on your purse, without having an adult sense of what is a reasonable/unavoidable amount of money to spend.
In addition, if your son is 12 he is JUST going to start growing at a phenomenal rate! Starting this summer, I would guess

. I really think you should do your utmost to rent a cello at first, as even a few months will make a big difference, first to hand (and foot) size, and then to height.
Not sure about cellos, but 7/8 sizes tend to be less uniform than other sizes, so it's possible that a full-size would be OK for him. Viohazard moved from 3/4 to full-size violin well before he was 12 (gorilla arms).
I second DiscoPants' idea of asking a dealer about a temporary loan...this kind of loan goes on all the time through our local shop, though admittedly usually with older teens and adults.
On the other hand, I've decided that buying one full-size instrument to last a lifetime post grade 8 might just be a myth for a younger advanced player - even if they have a good ear, their tastes and their demands on the instrument (as the type of music they play changes) inevitably change. If you have to buy in haste, maybe abandon the attempt to buy "THE instrument" right now, and get a secondhand solid midrange instrument with good resale value.
Sounds as if the neck got smashed or crushed as well as snapped? Hardly want to think about it...