In a 5 gallon pot, maybe you could use a tea saucer as your stirring tool (or 2 of them, 1 in each hand.) I would think that would work.
Just be sure and draw the chunks slowly.
If you decide to do it this way, here is how you proceed:
Take a long knife and carefully cut the curds in parallel lines about 1 to 1.5 inches apart. Then cut in parallel lines running crossways so that you have a checkerboard appearance on the top.
Now take your saucers, and carefully dip into the vat at the far edge, against the wall. Slowly draw toward you and this should pull up the bottom.
As the big chunks come up from the bottom, use your saucers to chop them into smaller pieces. Continue until all the pieces are 1-2 inch chunks and there are no bigger chunks remaining. When stirring, you might slightly change the point where you put the saucers in from time to time to ensure there are no pockets of big chunks trapped down there.
This all should take a little over 5 minutes, maybe less with so small a cheese. Don't fret the timing, go slow. After the curd is in even chunks, continue to stir until the whey is no longer white (this is what you do lacking a pH meter. This is how I learned to do it. I never have measured the pH) Total, this should happen within 10 minutes of first cutting the curd. The whey should be a pale yellow, but not too yellow.
Once this has happened, take whatever tool it is you use to cut the curd (maybe a large whisk? I doubt you have a Swiss harp) and stir in a gentle 8-pattern. At the beginning, you can use more of a circular pattern but this is trickier, I recommend you use an 8-pattern. It should take you about 10 minutes to cut the curd down to final size, and using this pattern they should end up evenly sized. (Stirring the big cheese with a Swiss harp involves a lot of technique, it is really hard to describe and maybe wouldn't work as well in a flat-bottomed pan) If your curd gets to final size and even size much faster than this, then you stirred it too aggressively.
After the curd is the size you want, take you saucers or a wide spoon and very gently stir for about 30 minutes. This we call brewing the curds (actually, in German we just call it Rühren, which means stirring) It is important that you do not let the curd come to rest (I don't know why some recipes say to do this, it is a bad practice) If you do, they clump and you will have to break them to get them apart again. keeping them gently stirred constantly will keep them from clumping, and keep them the size you want them.
Brewing the curds makes them strong and ripe, and prepares them for the scalding stage (in German, this is called vorkäsen). Now it is very important to keep them moving. As they heat up, they will want to stick fast to each other.
It is also imperative that the Vorkäsen be done in the proper amount of time, this is the number one determiner of the hardness and texture of the cooked Swiss cheeses. A little variation makes a lot of difference.
As a rule, I was taught that it should take as close to 40 minutes to reach the cooking temperature as you can possibly manage. This will take some practice, and is very difficult to get right the first time. I think maybe this step is easier to get right over a wood fire than it is on an electric or gas stove. If you get there too fast DO NOT continue cooking until the 40 minutes is over, you just need to remove the heat right away, and stir for maybe 1 or 2 minutes. When removing the curd, you need to be as fast as you can. On the Alp, we take a cheesecloth and with our arms dip in and remove the whole mass. It takes 2 or 3 times to get all the curd, and by the 4th time anything left is too hard to put into the cheese, and you just eat it right away.
Likely the biggest variation at the cooking stage is that an emmentaler will cook to a slightly lower temperature. We cook our hard alp cheese to 125 degrees, an emmental cheese is usually only cooked up to about 121 or 122 degrees. This makes our cheese a little drier, which also helps prevent the eyes from forming (we don't want the eyes)
There are a few option to customize the texture and character of your cheese. Do you want a true Swiss style Emmentaler? Then you want to make it hard and press it well to get very big eyes. Do you want a more American style Swiss? Then cook it to a little lower temperature, so it will be a bit softer and have smaller eyes.
The true Swiss style will age better, and an 18 month Emmentaler is a fantastic cheese (though not near as good as a 2 or 3 year Alpchäs) A more American style (softer) is more suited for a brief aging period (like 90 days). (There is a lot of opinion in this, I know)