I have raised jerseys for over 30 years. Steers for beef, heifers for dairy as nurse cows and some for a farmer as replacements. I know of no magic formula to get them to "fatten before they get the big frame" and don't know of what you are referring to as a big frame. I have also raised holsteins and brown swiss. The swiss get the biggest frame and there is no way to get them finished at 13-14 months. Don't know of any of the mennonites here local, that feed holsteins that get them to finish at 13-14 months either.
I now mostly raise and finish jersey steers on grass/pasture. Most will hit 1100 lbs at about 24-26 months and have a good degree of marbling. I will feed a little grain, like 1-2 lbs a day, for the last 2-3 months, for those that want it, which will add a little fat but the grass has to be GOOD. They don't get a big frame.
The thing with any dairy animal is they will, and even beef animals, grow first and then put on flesh. The bones/frame will naturally grow to what ever their genetic code determines. One reason why swiss are not really liked for feeders because they are slow growing....nature of the breed.
Yes dairy animals will get a pot-gut, when someone tries to get them on just hay or any lower protein roughage. They have been bred over the years to where they REQUIRE more protein and that means some type of grain and/or concentrate. Too much too soon and they will also get a potgut, as well as have all sorts of problems.
You have to have the frame so that the body can grow the muscle and then deposit the fat. An immature animal will be tender but it will not have the intra-muscular fat until it hits a certain stage of maturity. There can be fat deposits on the body but the tenderness and the flavor will come from the "marbling" which is really just fat that is distributed throughout the meat. Diet does play into it, but a roly poly fat 12 month old will have deposits of fat and there will be a smaller proportion of meat than a finished animal at 18-26 months.
The younger the animal, the more "tasteless" the meat. Flavor comes also from some maturity and that goes hand in hand with the animal reaching near its' growth potential then putting the growth into the added meat and fat. Veal is the most tender and "BLASE' , tasteless meat" there is. That's why it is cooked with lots of sauces, spices etc. Sure you can cut it with a fork. I custom raised veal for several years, the calves were drinking 5 + gallons of milk A FEEDING, and were fat as ticks but that white meat didn't do a thing for me.
I have to agree that if you are wanting an animal to " finish" quicker, you are way ahead to go with a beef animal. But a jersey beef properly fed and finished to the right amount of ""FINISH"" is about the most tender and tasty beef there is.