O. K. first lets get the terminology right if we are going to use it. I think you are confusing negative reinforcement with positive punishment (positive is giving something, negative is removing something), actually a "time out" is negative punishment. (denying him access to something he wants). Negative reinforcement is using a stimulus the animal does not like and removing it when he does what you want. Positive reinforcement everyone understands (treats or praise as a reward for doing what is wanted). Positive punishment is an aversive which can be mild or severe. Timing is important in all forms of operant conditioning, but never more so than in positive punishment.
So, in your situation, the problem is that leashing and removing the dog from the situation is negative punishment that he may or may not associate with what he did. By the time you intervene he may not connect it with his behaviour, and even if he does it can work against you because next time he may "evade capture" when he knows he has done something to displease you. Positive punishment after the fact, which seems to be what the Doberman owner was suggesting, is inappropriate and unlikely to work. Immediate positive punishment, if you can pull it off, does work but timing is critical. Dog parks are tricky situations, and sometimes the only safe option is to avoid them or in your case at the least avoid them when the tempting fluffy pups are around. The onus is on you to keep the fluffys safe, and if you can't then you need to stay away.
If you are set on using the dog park, I think you should work on your recall so that your dog is likely to come when you call. This is a particularly difficult thing with hounds, and with Basenjis it can be hard to get a reliable recall, but personally I think it is essential if you are going to let him off leash unless you can control his surroundings. An e-collar (shock collar) can be helpful to teach a recall, but I do not recommend it unless you are committed to learning to use it properly, which would NOT be for positive punishment, but rather for the aforementioned negative reinforcement (a low level stimulus that goes away when he responds correctly), and you do need to know how to train this effectively. The only time an e-collar should be used at higher stim levels is to protect the dog by breaking his concentration if he is chasing something into danger, and then only momentarily. And yes, if you use it this way it will hurt and he will likely yelp, but it generally gets his attention so you can then recall him. E-collars have a bad reputation because people use them inappropriately. For that reason, I generally avoid recommending them, and I only brought it up on this thread because you mentioned it, and therefore must be considering it. Do not go there unless you get some instruction in proper use.