But I believe now that they are not accurate, I should instead use a tool which I installed one that is a stratum ping tool. I read it pretty much preforms the exact task a miner does to send packets to the pool and returns a ping.
Correct, stratum-ping will be an exact representation of the work sent/received between you and the pool, I did mention in one of my old posts that stratum-ping could sometimes yield a very different result than using just ICMP aka ping, but I would like to state that in most cases the result will be exactly the same, so unless it's easy to perform stratum-ping (which is) it may not be worth the trouble.
Furthermore, your miner status page (assuming you do use a proper miner and software) would report what's called stale shares, that's the most accurate way to read latency between your miner and the pool, A high stale rate means there is a quiet large delay in the communication between the miner and the pool, there is no universal figure of what is accepted, but I'd say anything below 1% between stale and rejected suggest that your overall mining operation is good and you shouldn't worry, if it goes above that, there is certainly something wrong somewhere.