Why not the Gallican Rite? Or the Ambrosian Rite? Or the Mozarabic Rite?
The Sarum use of the Roman rite is the easiest to deal with because it has had the most work done to be able to celebrate it in english (or latin) with all original rituals and music in tact. The Sarum use is one of many pre-1570 roman uses, thus compared to the Gallican, Ambrosian, Visigothic rites, it is the closest to the Tridentine. It has the most similarity to Tridentine while also containing the richest most interesting propers and calendar of saints, any of the local Roman uses is potentially what the Tridentine would have become if it had not cut off organic development from forming it. One could use any other pre-1570 use instead of the Sarum as an alternative in theory yes, such as that of Paris, Mainz, Salzburg, Estergom (Hungary), Spoleto (Croatia) . It is the fact that it is pre-1570 that matters.
The Gallican Rite, which is almost a variation of the Mozarabe (Visigothic) rite would probably need to use the Mozarabic propers, as it does not have its own surviving ones. The Mozarabic propers are however somewhat 16th c. reconstructions, they are not available very easily either. The genuine Mozarabic propers exist in one, two or three manuscripts, but for whatever reason seem not to have been transcribed into modern notation. I recall that some of them are not legiable, but than some are definitely preserved in the early diastemic chant notation with 4 line staff . I really cant say about that, it seems to me it is somehow possible to use authentic 10th c. Mozabic music if the right person investigates it (not an easy task though). The Mozarabic divine office has very rich hymnody for both the proper of time and proper of saints which makes it quite worthy of orthodox usage.
The Ambrosian is probably the most practical to use because it remains the most intact and with all the complete music and melodies, no questions asked.
You can download a 19th c. transcription from Solesme monastery of an actual 12th c. Ambrosian Antiphonarium (For both Mass and Divine office use) at this link:http://archive.org/details/palographiemus1900gaja
That would be easily useable at an Orthodox Mass today, so long as the Latin is acceptable.
The Roman rite in any of it's local uses is the most established rite, it is the most familiar to the widest variety of people, contains the largest selection of liturgical books from the 9th to 15th c.
It's not that the other rites don't deserve revival, but..the motivation to create the books in languages besides latin or to use them at all is not as great. It's practicality more than anything. If one feels strongly impelled or attached to those rites wants to use them, I would happily support them in any way possible.
Many will say the Sarum itself is impractical...well perhaps compared to the later abbreviated forms of the Roman rite, but the important work of having it available in english and having the books available to download online is nearing completion.
In fairness much of my concern is not particularly about the words of the Mass itself.
Other than forgetting about the bidding intercessory prayers before Mass, I have no objections to the actual Tridentine Mass, even the 20th century form. It is able to be seen as Orthodox, no question, the extent to which it was artificially altered at Trent is very minimal.
Much of the main difference with the pre-1570 local Roman uses and the earlier 20th c. form is that they have a much wider range of propers and interesting music and ways that the calendar works, more octaves and what not. This is perhaps the heart of the matter to me. If for example you compare the hymns of the Benedictine Monastic Diurnal from lanceloteandrewes press to the 1534 Sarum use hymns (thus also any other pre-1570 use) you will see a very big difference. The benedictine omits a great number of beautiful hymns, it actually has 30% less, with the Mass there is a similar situation.
Many anglo-catholic (anglican/episcopalian) parishes , including a few still today (I'm thinking of Mt. Calvary in Baltimore, MD specifically, even though they are now with Rome) they would follow the Sarum calendar and propers even though they would use the 1955 roman rite in english for example.
I personally would also have no objection to using the later 19th/20th c. propers for the feast of St. Joseph , Christ the King or Most Holy Body of Christ within a Sarum mass or office.
This is as simple or as complex as you want to make it.