Asking a slightly different group of people selected by the same systems and culture that gave us HS2 is unlikely to result in the cost savings we need to make rail construction costs politically palatable. The line speed of the track is about reason 43 as to why HS2 was so expensive, the leading reasons are basically that our construction industry is pretty inefficient and our planning system slow and disjointed.
One of the best examples of how to do big stuff is the US Ballistic Missile program in the 1950's (they built 3 types of ballistic missiles and fielded them in about 5 years), the general in charge mapped the process to try to work out how it could get done but then essentially demonstrated that it couldn't be done with the existing process. So they ripped up the process where they could and used work arounds where there was statute law in the way. That is how you actually get stuff done, old systems need to die.
If you actually want to do high speed rail the following is probably required.
1: Have an actual strategic plan, e.g. national strategic network which connects all conurbations with 500,000 people to 300kph high speed rail, those conurbations all have a mass transit system, everything over 100,000 has a 200kph connection to the network. GBR should do this, said plan could actually be created in about 2-3 weeks if you really wanted to.
2: Appoint some people who have actually built some infrastructure quickly and cheaply (in global terms, not people who have sorted CrossRail), e.g. get the people who built AWS or similar, pay them what the market demands, let them hire who they want, sack them if they don't work. The rail industry people are there to solve problems not to lead, at least not until stage 5.
3: Do what the people who have built AWS advise, particularly re: scheduling, funding method, contracts and where technical expertise is built.
4: Have a rapid escalation route when what they want to do conflicts with other government departments, all of them have royally messed up so frankly they should defer to he methods that have been proven to work. The project is being done for the government, it can change the law and in most cases a minster can overrule or expedite virtually every process. You can do things quickly if you want to see COVID measures, and in this context quick also means cheap.
5: Start off with a containable project with a willing local or regional area, success breeds momentum and authority. Rinse and repeat.
This should actually be a core government policy, HS2 is part of the national malaise, "we can't even build a railway" is one of the most frequently quoted reasons for despair with politics. Actually demonstrating that you can build a railway is actually more politically important than the actual economic benefits or costs of the railway itself.