Hey Bill, welcome to the site and congrats on getting your hip done. I'm sure a lot of our current hippies will report in, to let you know what they're facing and what you can expect.
One piece of advice I can give you is to be patient. What you are dealing with is a recovery of bone, nerves and muscles; while the muscular development is important, allowing the bones and nerves to heal is crucial early on.
I understand feeling like you want to do more - being able to do the muscular exercises with ease is a blessing and helps your recovery greatly. Remember that the bone has to heal, otherwise no amount of muscle will keep your device intact. We have stories here of returning too early to activities that compromised the surgery.
I returned to work at a desk job by five weeks. If that's the type of light duty you're talking about, then given that you're making a good recovery, I would think that 30 days would be ok. My surgeon restricted running until one year had gone by, some others allow it earlier. You're probably talking full recovery by that time, but you will be fully functional for a lot of other activities long before.
I work with the military. I know the pressures put on you and the expectations - friends on mine have trained with me to pass the fitness tests. I guess it comes down to what light duty is defined as in your job.
One thing I wanted to address here is that you feel like you're malingering. The effort you're putting in is appropriate, given that you need to support the bone and structural healing that's happening.
Given your good attitude, when it's the proper time for hard muscular work I have no doubt you'll put in the hard effort, but in the case of early healing a hard muscular effort could compromise you. Get that hip healed correctly and you'll be running just as hard as some of our hippies - but let it heal. Not an easy thing to do, to be patient but it is, I believe necessary.