The actual displayed digits with the CNT-90 varies with quantities of samples and measurement stability. If your signal is stable enough and you keep measuring, 14 digits will happen if your signal is super stable, but if it's varying by enough measurement to measurement, it will only display down to the least significant digit above the noise.
In terms of actual timing, you want to look at digits per second (and basically everything mentioned is 12 digits/s), and then timestamp resolution (100ps for the CNT-90, 50ps for the CNT-91, 20ps for the 53230A). I don't know of a commercially available counter that can give you more than 12 digits/s or a smaller timestamp resolution. Then the additional digits are all up to software averaging, and if you wanted an arbitrary number of extra digits worth of averaging, it would be easy to do with a little custom software (though it would be only useful above the noise threshold of the variation between signals).
I think the CNT-90 based counter that's your fallback is overpriced. The CNT-91 series units have been going for around 2k USD for a while, and there have been plenty of CNT-90 based counters that have gone for half that or less (though maybe not in the last few months, there's not a ton of volume). I know it's harder to find stuff in the UK, but I think a really good deal for a CNT-90 based counter is about half what you're considering - maybe something in between is more realistic, but 1700 pounds seems a bit steep from what I've seen of the market.