When I started driving trucks, back in the 90s, I came up against the same experience block. A couple of places I had worked at as a forklift driver had gone bankrupt, so I just changed my job title to lorry driver and said I had drove a 7.5 for them. As soon as I did that, I got the next job I applied for.
Unethical I know, but there’s nothing to stop you finding a couple of local companies to yourself and rewriting your cv. Whatever you decide, act quick. The work has dropped off already and will be dry for the next few months.