Dianna, you didn't open a can of worms, you opened a whole slab of them! The question of why 171700 had its ARN changed and 699 didn't could be due to any one of a number of reasons. Reading Mikes comments about the block of ARNs allocated to engineering equipment, it may have been that the block was exhausted at that time. and 699 couldn't be allocated a 164 number. The question then is why did 700 change? It may be that the sprayer used on 700 was transferred from another vehicle with that ARN. The sprayer would be a complex piece of plant and would have a log book and service record of its own, and for continuity it might explain the ARN switch. If 699 had a new sprayer fitted then the truck would have kept its ARN, especially if the Engineers block of ARNs was exhausted. The later sprayer trucks kept their own ARN like 699 too. It might be that there were no more numbers available in that block and there was not another block available, or there was a simple change in policy. It is really all speculation, but someone may come up with an answer.
There is a problem with the description of trucks in the records, as there is a lack of any hard and fast rules as to when the description is accurate. 171699 and 700 were produced as cab chassis, but are described as sprayers in the records, but the Mk3 tippers are described as truck chassis as produced. We know that they were disposed of as tippers, but it's not reflected in the records. That's why it was so hard to track them down.
It might be an idea to search the SVN records for 699, it might be there and slipped under the radar because it was listed as an F1. I've just come across some published photos of SVN trucks and some of the ARNs aren't on the database, once I've had a close look with magnifier I'll post them. Anyway there was some good teamwork on this one. Keep on keeping on.