I think that raising up some steers and selling as beef would be a little better deal for you ... if you have the contacts to sell the beef. I raise a few to sell each year. Mostly jersey or jersey cross, steers. It flucuates and I get tired of dealing with people who want it, then don't have the money or want you to finance it... or change their mind when the steer is already hanging in the butcher shop.... Mine are 99% grass fed, I will feed a little grain the last month to get the animals to come into the catch pens but by no means are "grain finished. Don't push it as much as I did but it can be a good source of extra income. Make sure you check your rules... we sell "live beef" on the hoof, but most take a half so we co-ordinate the buyers so to speak.
I am not saying grain fed is bad, I just like the taste of grass fed better. But again, jersey and guernseys have a yellow fat and a little sweeter meat so a different flavor. They both do marble good.
If you were to buy something in the 700 lb range in the spring, get it on grass and gaining weight good, then it could be butchered in late fall at 1000 or more lbs. Hoping for a gain of at least 2-3 lbs per day average, would get you about 10 to 1100 in 6-7 months. If you grained the last 45 to 60 days, the animal ought to put on some decent weight. But again, what is your carrying capacity of the pasture? Here we figure 1 cow/calf pair for 1 1/2 acres per year, on a good year for rain and grass, so a beef steer would be like maybe 1 per acre or maybe 1 per 2 acres? If you wanted to stagger them, with the hay through the winter, then you could get away with a few more of different sizes, and replace the ones you sell with smaller ones....
Technically the grass farmers, that graze animals, figure on a carrying capacity by weight rather than by head, but this gives you some basics. If you really want to do something like that, get a few copies of the magazine Stockman Grass Farmer, usually can find at TSC and do some reading.
I think it is great that you want to utilize the grass in the pasture on the farm, and there are ways to do so. You don't have to get big, and maybe a small "freezer beef " operation would fit in with what you have available. There are books available for you to read and learn from others experience...you don't need to re-invent the wheel, but pick up from what others learned by doing, and making their own mistakes, so you don't have to make the same ones.