Hmm it's surprising you cannot use the modeler at all during consistency checking, it should be run in the background.
Your computer isn't that bad but on large models there are many checks so it might become a bit too much for it. That said, we haven't profiled consistency checking for a while so if you're willing to share your model (file a ticket) we could maybe do some profiling on it to see if there are quick performance wins.
To make modeling a bit easier for you, you can increase the auto-check delay which is a feature for slower computers or very large models. You can find it in the preferences.