Once again, thanks for all the really helpful input each of you have offered. Don't think I cannot see the non-mini side of the argument... I want to embrace it and I want to like it, and it tears at me that I don't seem to enjoy it. I already run my games with all kinds of fudging for the sake of keeping things fun and interesting... it's just keeping the entire scene in my head that is so daunting for me. I'm so forgetful and distractable... and without the mat and minis, the entire group is relying on me to inform them of what is going on. That's a terrifying load of responsibility for someone like me.
I guess I'm just anguishing needlesly. I don't expect anyone here to solve my problem, but I really do appreciate being heard and understood.
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Great thread topic. I agree with everything Kamikazi said. I'll add few things.
1) Gridless need not equal mapless.
Describe the location, be evocative, and mention some details. But, if there is going to be a lot of movement, we always drew the room and gave rough indications of where things are and its size. This helps everybody visualize and keeps people from asking the same questions over and over. It need not be a big drawing and we usually just used a quarter sheet of paper. You could draw each room on a notecard and give it to the players as necessary.
2) As a DM, be fair. As a player, trust the DM.
Since many things are judgement calls for the DM, it is really important that everybody trusts these judgments. Like an umpire in baseball, you won't always get it right, but you have to be do your best for both teams. In high school, I admit I was vindictive towards a player I didn't really like and always called borderline cases against him. Petty and it ruined the campaign.
So, if the halfling rogue wants to duck under a table and tumble into a flank position, make a reasonable call. Is it too far? How much does the table and tumble slow her down? There isn't a right answer, but don't let the monsters get a different answer than the PCs.
It sounds like you have a good group, so this shouldn't be a big problem.
3) Tactics require action and details.
A tactical player will hate gridless combat unless there are lots of possible actions and/or detailed terrain features. This gives them (and you!) the ability to create meaningful strategies without having clear movement rules. For example, a bunkroom for hobgoblins is boring. A bunkroom featuring a stack of ale casks to be toppled and a cooking pit to be pushed into is interesting.
It isn't anything you probably don't already have on your grid... you just have to be a little more explicit since it is mainly verbal.
4) Do the things you can't do on a grid!
Big battles, a chase through a forest, a slide down a mountain, etc. You could probably make each of these work on a grid... but the time commitment for drawing can be big. Use this extra time to flesh out details of these places, describe it, and move on.
Seems like you are a fun DM, so don't let gridless spoil your fun. Go back to the grid if you have to. But it can be fun without it.