New Manager - Fast Paced Shop

I know where you're coming from, feeling like MT guidance doesn't really "fit" with what you're doing.  Most of the examples are for a corporate office environment, not "on the floor", and so it can be harder to relate.  The core principles that MT teaches, though, are grounded in humanity, and you're still managing people, even if they're not sitting at desks in a high-rise building.
My recommendation for you is to go back to absolute basics.  Listen to the one-on-one podcasts from the "Basics" series again, and really reflect on what they're trying to achieve, regardless of the setting.  It's all about relationships.  I get the sense that you've got to start from here, because of your comment about feeling "disconnected from my team".  The fact that your bosses are pressuring you for change suggests you've got a lot of work to do, but you're not going to achieve meaningful change without the support and help of your people, so you've got to get connected with them first.
If I were in your shoes, I'd start by listening to the O3 casts again and thinking hard about them.  Then get your team together in a "toolbox talk" or similar, and explain that you're going to "reboot" your relationship with them.  Be humble, and open about what you've been doing wrong.
Then, spend the next few weeks just talking to people.  Your O3s are a big part of that, but just being visible on the floor in a calm and positive manner will also help.  If you're not usually out and about, people are going to be nervous as all hell about you being there, so resist all temptation to criticise or otherwise "get in the way".  Just watch.  Smile.  Say a few times, "you're doing a great job.  Thanks."  I recall hearing in at least one MT cast about one manager who rotated through everyone on his team, one person per day, and singled them out for a few kind words -- he'd take a couple of minutes to ask how they were going, what was happening in the work, and thank them for their contributions.  I wish I remembered which cast it was from (it might even be the O3 Basics), because I'd recommend listening to that story.
Take an interest in what people are doing.  If there's anything happening you don't understand, swallow your pride and ask questions (when people aren't in the middle of things, of course).  Again, be humble about it, and resist every urge you have to make "suggestions for improvement".  You're not there to make anything better, you're there to learn.  Even things you think you understand, take some time to learn more about them.  I'll bet you learn something you didn't know from every single person you talk to, every day.
Meanwhile, your management will probably be riding you hard for change.  You're going to need to "sell" what you're doing a bit.  Explain that you're cognizant of the need for change, but that all change is made by people, and you need to get in better touch with your people before you can successfully lead them through the change that management are looking for.  You can show them you're making progress by identifying changes that can be made (you'll get plenty of great suggestions from your people once they start talking to you).  In the times you're not on the floor, you can work on plans and prioritisation of work to implement some of those changes, and that work can show your management that you're thinking about and committed to improvements.
One final thing: if at all possible, get along to an EMC/ECC (the Manager Tools conferences).  They're amazing days of learning, and you can ask questions during the day which will help to fit the MT principles into your specific situation.
That's probably enough new work to cover you for a month or so.  Good on you for recognising the need for change, and please let us all know how you get on.  I'm sure amongst the collective wisdom of the MT forums, we'll be able to guide you along the entire path to awesomeness!

My directs run field service teams and are out in the field much of their time. We still do weekly one-on-ones, scheduled to fit neatly into their work week.
For example, one direct is local and our O3 is scheduled shortly before a weekly meeting when they have to be in the office anyway. The other direct is remote so we do theirs over the phone, so it's normally irrelevant whether they're in the field or in their office.
The key is flexibility - be prepared to reschedule when the work load doesn't allow having the meeting at the appointed time.
Steve