There certainly will be overlap between the RDLs and good mornings. You should alterate between the two and not perform them on the same session. Also, there is the option of reducing the volume on deads to make room for either RDLs or good mornings OR even replace a dead session with a RDL session.
Perhaps a competitive power lifter can chime in on this. I would think the RDLs will allow you to get in extra volume on your grip work. Also, you mention an anterior pelvic tilt. It's not unusual to see this go up the kinetic chain this manner: anterior pelvic tilt -> excess lordosis at lumbar spine -> inability to extend at thoracic spine. Now, I'm not saying that you're suffering from this (impossible to tell via an online forum). However, if you are unable to properly extend at the thoracic spine, your scaps (shoulder blades) will most likely be in an anterior tilt as well. This means you may not be able to properly retract and depress the scaps when the bar is at the base of your neck as in the good morning. Long story short, perhaps the RDL is a better accessory lift for you at this particular stage.
I don't know if you remember Scott Abel. He used to post some fascinating articles on this site. Now, let me first say that I do NOT agree with every thing he says. However, he did come up with an amazing exercise that takes a great load of stress off the lower back while working your grip and hamstring complex.
The first two thirds of the vid shows the basic TRX hamstring workouts. Towards the end, you'll see a movement that is surprisingly effective. Obviously, you do not have to use the TRX, any strong webbing and handles will suffice.
A well known strength coach who has been recently posting articles on this site does a variation on this in which he includes a reverse row. A good movement. What's amusing is that he implies he invented this recently. Well, if you look at the date on the Scott Abel you tube vid, it shows 2009. And who knows...? It could be that Abel "borrowed" this from someone else as well.
Regardless, this is a viable option for you. I've done it. I've had my clients do it and it works quite well. If you find your grip going use straps or hang those ab slings on the handles.