P.M.
You give so many mamas and grannies something to look forward to as their babies turn grow toward toddlerhood! Some kids just have much stronger wills than others. It sounds as though you are really doing your best.
I would try two things. One would be a behavior modification chart, or maybe even two charts: one for cooperating when leaving the activity, and one for reducing the screaming. Both of these will require that you notice and appreciate as many occasions as possible when your child is NOT engaged in the undesirable behavior, so this might take some real effort and "training" on your part. Give him a choice of stickers or colored stars to put on his chart every time you acknowledge him. Giving him strokes for being calm and cooperative can add real value to those behaviors for him.
The other would be to work out a CONTRACT that he can actually sign (with a pencil, thumbprint, or sticker) before you leave for the activity. Make it clear that you are doing the activity to make him happy, and in return YOU NEED him to try to make YOU happy, too. There can be a reward for compliance that you can agree to ahead of time and give him on the way home, and a consequence for tantrums, such as no more special outings for some length of time that you think would be meaningful to him. Work it out together, ASKING HIM WHAT HE THINKS WOULD BE FAIR if he were the parent. Put it in writing, read it to him, ask him to summarize if he is able, ask if he agrees, and then ask him to sign it.
Then, before you leave your driveway, show him the contract, and if he is verbal enough, ask him to repeat what the agreement was. If he can't express that, read the main points again and ask if he still agrees (if not, stay home). Before you unbuckle him at the destination, do the process again. Halfway through your activity time, repeat again. Five minutes before leaving, repeat, and remind him that HE AGREES that you need his cooperation, even though you know he would really like to stay.
Then, if the meltdown occurs again, follow your usual pattern, and remind him after he calms down that he knew what he agreed to, and you are sorry that he chose to behave otherwise. Now you won't do anything special for awhile. AND you will give him a chance to try again in X weeks.
I helped a mom implement this contract process a few years ago. By the third or fourth cycle, the negative behavior became much more tolerable. It's hard to know if her daughter would have passed that phase anyway, but we both sensed that the contract was helpful.
Just thought of a couple of additional points.
(1) If you use the contract, let your son watch you employ contracts with other family members, too. You and your husband can set a great example of how delighted everyone is with a successful contract.
(2) Consistency is incredibly important when dealing with a behavior you want to change - you probably know this already. But if you give in a little bit sometimes, you will set yourself up for a long, slow struggle.
(3) Observe whether you give your son as much latitude as possible in everyday family life. Give him as many choices as you can, and periods of completely free play if this isn't already the case. Young children have so few opportunities to exercise freedom. He may have less-than-average tolerance for being controlled and manipulated, and it could be that the events you describe are the last straw for him.
(4) While he is throwing a tantrum, do not let him see you react with anything but patience. Some kids gain a sense of power from pushing their parents' buttons.
Good luck.