It's tough to switch the mixed grip hand positions from one way to another, it just makes me feel off balance and doesn't do much to keep my form solid.
Hook grip is great, but it takes time to get your thumbs used to the pain level that comes with heavy weight. I hook gripped a 1-arm deadlift with 375 once, and I was sure my thumb was about ready to explode midway through the pull. It works, but expect to take about 5-10 sessions of deadlifting with it before you'll adapt to it, though athletic tape around the upper thumb joint can help a little. Also, with hook gripping, DON'T just let the weight of the bar fall on the thumb pad as you pull - part of alleviating the pain factor is to wrap your thumb around the bar first, then tuck it in deeper at an angle instead of straight, so that you can feel the bulk of the pressure in the middle of the thumb joint where it will cause the least discomfort. Again, takes some practice and getting used to (and yes, you'll often shred the skin at the base of the thumb pad, that's just how it goes), it's just a matter of time.
Though, overall, if you're only deadlifting once per week and aren't using a mixed grip for anything else like shrugs and such, most people aren't going to have imbalance issues over the course of a few years of deadlifting. Lots of people have pulled mixed grip for decades and stay balanced, most of that comes from keeping ALL upper body in proper check, making sure not to neglect chest, shoulders, traps, lats, rear delts, rhomboids, etc. with all the other good stuff like heavy benching and rowing, overhead pressing, etc. More often is a general muscular imbalance that will cause problems vs. just using the mixed grip for deadlifts, so as long as you're maintaining everything else properly and don't feel like things are "off" on any of your lifts, you should be good to go.
Chalk WILL make a difference, not always a huge amount (it doesn't magically add anything to grip strength), but ANY perspiration or oils on the hands will reduce the effectiveness of your grip and will reduce how well you can hold on. Chalk simply takes out the X factor of anything that could reduce how well you can hold on, so if your gym allows it, it's a good thing to keep handy.
Otherwise, you can just work to incorporate extra grip work into your routine a few times per week. I always suggest it at the end of the workout, a few sets of static holds in the rack (basically, set the pins for a really short 1-3" deadlift, pull to lockout, and hold it for time). I loved doing 3 sets at the end of my upper back and deadlift days each week, load up your 1 rep max deadlift, and hold that sucker until it drops out of your hands. If getting the weight up gets tough, you can also use your thighs as a support to get the bar up a bit by pulling it back into your body vs. trying to do a normal short-ROM deadlift. You can build ANY type of grip this way, either mixed grip, double overhand or hook, do this twice weekly until you can hold your max DL for 30 seconds without any problem, then start adding weight. If that's too heavy and you want to build your double overhand grip, try something like 70-80% of your max until you can hold it for 30 seconds, then work toward 1 minute, add weight once you get to your goal.
Definitely not rocket science in this, sometimes you can get ahead with things like grip by throwing precision programming out the window and just beating your body into submission with heavy weights. Once you get to where you can whistle your way through multiple sets of holds with 500+ lbs., you'll have a grip that won't fail you when you need it most