I made a lot of money moving mid size enterprises from legacy ERP systems to custom in house ones.
The DVLA dataset and the computations that are run on it can be studied and replicated in 3 months by a competent team. From there it can be improved.
There is no way that this system requires 13 hours of downtime. If it required two hours - even if the code was generated through automation it can be reverse engineered and optimized.
It is absolute rubbish that this thing is still unavailable outside of 8am-7pm.
I maintain my position that it could be replaced in 3 months.
I got my start in this business when I was in university and they told us our online learning software was going offline for 3 days for an upgrade. Those are the gatekeepers and low achievers we fight against. Think bigger.