Perhaps I could add some comments that may be of assistance or of interest.
Conversion
The Offshore Fund regulations contain specific rules that disapply the standard UK capital gains tax rules that might otherwise have allowed the conversion of a non-reporting class of interest into a reporting interest to be treated as not being a disposal. In other words, such a conversion is treated as a disposal.
Remittance basis election
Rayg could consider selling the non-reporting funds in a tax year where he makes an election to be treated as being taxed on a remittance basis. The remittance basis election need only be made for that single tax year. There would then not be any UK tax provided the funds (or anything later representing the funds) were remitted to the UK.
There would be the other disadvantages of claiming the remittance basis, such as the loss of the personal allowance. The election might not be available if Rayg were a long term resident, or might require him to pay the remittance basis charge.
Donation of funds
Guya makes an interesting suggestion if Rayg wishes to use the funds to make charitable gifts to a dual qualified charity. The structure of a dual qualified charity is that there is a US charity which owns a UK charity. The gift is made to the UK charity.
For UK tax purposes, it would be intended that the gift falls within the rules which broadly provide for a form of Gift Aid on the donation of listed shares and interests in mutual funds. A gift of non-reporting funds should be capable of falling within these rules. The points that would need to be checked are whether the gift would not trigger any charge under the OIG rules on Rayg and the tax position of the charity on a later sale of the mutual funds.
My understanding is that the US has similar rules, but subject to different detailed considerations. Perhaps others could add comments on the US position.