As a goat keeper and a commercial sheep farmers wife and knowledge of terminal sire sheep breeder I agree with scotsgirl and ankes posts. Even if tied up goats a very good at handstands, and if lambs do get their fill the udder probably be wrecked before lambs weaned. Wouldn't be many goat keepers would sell for this use for their goats welfare, That's never mind your client learning the care of the goat which is different to sheep. Most people are on the BGS testing scheme which is cheaper or some large closed commercial herds are accredited or those that are already accredited with their sheep.
I hand milk my goats twice a day and stock up the freezer in advance prior to lambing and split the milk between goat kids and lambs that need a top up and those that end up as pets, by bottle feeding or the lamb feeding box, To make life easier the shepherdess ad lib system is good for pedigree stock and goat milk works in it if you keep it clean. Lambs do better on goats milk than milk replacer and has saved many of our lambs. Although Downland now produce a lamb milk replacer made from sheeps milk.
From what I understand from you post your client wants to have big single tup lambs as singles grow bigger first with the extra milk. One thought I have is since they are using embryo transfer they would be better considering the recipients be friesland or proven milky ewes leaving the lambs on. Some of our texel ewes are quite milky and easily rear twins and some triplets, The key to rearing the pedigree lambs at higher growth rate as in single lambs is access to ad lib lamb creep from young age regardless of what milk they get. We used to have pedigree charolais flock, pet lambs with creep on shepherdess grew tups as good as the single tup lambs. We had a creep feed area that all the lambs could access as well as the shepherdess some of the lambs who had mothers copied the pets an got extra milk via sheperdess.