Stulte,

I'll let an Ordinariate specialist answer for sure, but I think it would be reasonable to use the Epistle and Gospel tones from the Liber Usualis.
What do you mean "not done at a Solemn High Mass"?

At Walsingham we use the tones as may be found in LU. There are Sarum variants, but, alas, I can't get every thing done that ought to be done. On all solemnities the prophecy is sung by a vested instituted lector who sits 'in choir', and the epistle by the sub-deacon.

There are also Sarum variants of the collect tones, with the celebrant ending on do-ti and the Amen being sung ti-do do. We should be doing this, too... but alas.

Matthew is, unfortunately, quite right about the English RM's version of the prophecy tone being all wet. I would never use it. Obviously, they either didn't know what they were doing, or deliberately produced an inferior work without historical reference. Someone told me that the botched final cadence was owing to the NO's 'thanks be to God', which follows, but I fail to see how this really makes any sense at all. At Walsingham we continue to use the tone in its historic form.

@Chris - what I meant by that question is that I was unsure if the readings were chanted during a SHM in the Ordinariate's Use. After posting this, I did some looking on YouTube where I saw a video of the Ordinariate's Mass according to DW:TM where the 1st reading was read, but the epistle was chanted which I thought interesting.
@Steve - Thank you. I'll send you a PM soon.

That's correct. It was at another church. That's interesting that the readings are spoken instead of chanted on "normal" Sundays. Is there a specific reason why?

You are both academically correct, and were I to be satisfied totally the lectionary would be sung always. I suppose that this is, in the minds of our decision makers in these matters, something that would be 'too much' - sad, but probably thought to be a needed nod to contemporary 'culture', such as it is. Even for the Easter Vigil, my suggestion that ALL the readings be sung, not just the epistle and gospel, that was thought 'too much'.

At least we have made progress and Bishop Lopes is firmly behind it. Walsingham has sung all three readings on solemnities for over 30 years, since it was founded, a regimen that I first introduced as the founding choirmaster. The very first thing that Bishop Lopes' recent predecessor, our first 'ordinary', did was to tell us to stop doing it. Utter betrayal! A stab in the back! The first thing we got permission for from Bishop Lopes was to resume doing it. (Actually, permission for this was the very first thing that Fr Hough asked for, whilst driving back from the airport at Bishop Lopes' arrival.)

It’s following the GIRM and Musicam Sacram. I don’t think there’d be a problem doing a Missa Cantata wherein one sings whatever is sung in the traditional Latin Mass and nothing more or less..

Well, in the defense of the 2011 Missal: it’s a proper tone, the ferial tone, which is inappropriate for 90% (I am exaggerating here) of sung Masses, because they are either Sunday Masses or festal. It should be used for Masses of ferias, and usually in Advent and Lent only, since you will probably not have a sung Mass on a green feria, which are rare anyways, and Masses for the dead. Oh, sung Votive Masses use the ferial tone too.

This should be a lesson to certain folk, and heartening to others who strive...
When we sing the readings the lectors are swarmed after mass by those who were moved almost to tears at the beautiful way in which the sacred texts were chanted.