You are absolutely right on all points. We buy some Spicy Bread and Butter pickles that we are crazy over. We just slice up some baby cukes about 4”-5” long and drop them into the leftover brine. They are much crispier than the bought pickles. I may not ever can pickles again.
If you want them done quicker you can safely leave them out on the counter for a couple of days then refrigerate. When I start a fresh batch of koshers they sit out for about 3 days, than it takes about a week after that in the fridge. I like to add whole garlic cloves too they will pickle too but it takes a little longer, you can slice them in half lengthwise too.