How to cook a pot roast without it tasting like vegetables
I think you've answered your own question. Browning and adding veggies later will both help. 

Browning doesn't "seal" the meat to keep flavor or juices in, but it does create a very nice flavor that's almost always associated with meat, caused by the Maillard reaction. I think browning could go a long way to resolving your flavor issue. 

This is a little counter intuitive of cooking with a slow cooker, but you can start the meat with a bit of water (or wine, stock, other juices) and then only put the vegetables in much later in the process. Of course, then you have to tend your crock pot, which is often not the point. That would decrease the time that the vegetables had to affect the taste of your meat. You could even experiment with which ones to add later and which to add at the beginning. If it's just the carrots that are offensive, that may be the only thing you need to throw in later.