Agree on US disengaging completely from Saudis, and in fact putting pressure on them as much as on the Iranians.
Britain is much better positioned to manage the ‘diplomatic’ angle - that’s Britain forte in general. But Britain also needs to limit their ‘other support’ to them. It isn’t only the Saudis, the Gulf States and oil there too are mostly in Shia areas.
In terms of Mecca and Medina, Jordan I think may be viewed as more of a legitimate overall custodian, because of the current king’s Hashemite bloodline. Bearing in mind that when the House of Saud was “nominated” as the custodian, it had to be endorsed by majority muslim countries.
Anyway, yes, that place needs to be confined to a ‘spiritual centre’, at most. Easier said than done. Mainly because Islam has always been very much tied to politics and military, unlike Christianity or Christendom.
Historically speaking, the British have been diplomatic fools in the middle east -- setting up evil with short-term gains. Right from the early 1800s when they propped up the Ottoman Turks instead of freeing Christians, to when they put Sunnis and Shias in a Christian Lebanon, to when in WWI they didn't attack at Antioch, when there was clear news of Arabs (under the Hashemites and secular pan-Arabism) and Armenians and Kurds ready to overthrow the Turks; instead they expended blood and thousands of lives at Gallipolli.
No, the Brits are an expended force -- let the Middle Easterners come under Russia and China and India's thumbs.
The Russians and Chinese won't be so nice -- look at Russia's brutal yet effective, people moving in the 1940s and 50s -- creating ethnically pure states.
They will slaughter all the non-Christians out of Lebanon, create Alawite and Christian Syrias, Christian Assyria, probably also a wider Armenia
Plus, the Russians will be kept busy for decades in the Middle East and Turkey -- no time or ability to cause mischief in the west.