Jonas, I haven't changed my tripod, head, plate solution from my past use. I have the larger Markins head--I think it is a 10L. On my other cameras I use RRS L brackets which do have a connection for a handstrap. I have an old Camdaptor with hand strap on my 400D---I couldn't see a way to use it with the G1 because of the way mine threads through the lugs--the strap that connects through the lugs won't fit the G1's--I'd be interested as to how you connected yours--can't tell from the photos.
So--for the G1/GF1 I have an old Wimberly AS plate that does cover the battery door but hasn't been an issue for me and fits quite well except being a bit too long--I just carry a little Allen wrench to loosen it when I need to change batteries.
I've checked RRS--and for the G1 they recommend a small bi-directional plate which allows for entry to the battery.
http://reallyrightstuff.com/rrs/items.asp?Cc=BodyPanaG1&iTpStatus=0&Tp=&Bc=
I'm a great fan of AS systems and find the Markins does not tilt with any lens (and assume the smaller ones are equally capable). What I do love about AS instead of Manfrotto and other QR systems is that it doesn't lock you into any system--usable with many heads, rails (I have the RRS focusing rail which I use for macro, panos, etc.) and a lot more flexible. You will be able to choose from a number of clamps (I don't use a QR--rather prefer a screw clamp), heads. And--there are a lot of plates available also--I haven't checked Kirk and others. Someone on this or another forum linked to a very inexpensive AS plate--but likely it does not have a slot for the handstrap---nor does the RRS bi-directional one just due to its design.
The upshot of this is---I haven't really looked for a better solution. I use the Wimberly on either the GF1 or G1 when needed, I use an optech wrist strap (not handstrap) with the G1 and moved it to the left side ala Godfrey who suggested that it was easier to change lenses--and I only use it for safety purposes anyhow--not to carry. With the GF1 I use the same Wimberly plate (but will likely buy another flat plat--there are a number available that will fit) and continue to use my Optech neckstrap shortened to clasp and make a small 'handle' that I wrap on my hand--and can add the neck piece if I want to carry around neck (the only camera I've even considered carrying that way).
I don't know about plates available for the m4/3rds right now--RRS plates in the past have had a slot for hand straps to be attached (I have the old Canon E1 strap on my 5D with an RRS AS L bracket). I just checked the Camdaptor site since it has a number with the AS plates, but none they recommend for the G1.
So--in the end, nothing to suggest. I'm okay with my system. I like the AS plate--whichever mfg. I'm less inclined to be interested in a handstrap for the G1 or GF1 so haven't looked for an AS plate with a slot--and I'm still wondering what handstrap has a connection to the top that will go through the G1's lug.
I would think that a Camdaptor with an AS plate (most of theirs) that has a connection to use with the G1 lugs and one of a number of AS clamps to use with a variety of heads would work--Both Markins and RRS would be good choices for heads/clamps. I just checked Markins and think the smaller ballheads would work fine. They have a bidirectional plate similar to RRS that should not cover the battery door. However, like RRS--it does not have a slot for a handstrap. That's the only issue I can see--finding a plate with the strap slot. Otherwise, I can recommend a lot of different AS sytems--I'm looking forward to Terry's review of her new system, but--for me--my old head/clamp/plates works well--I use it with 2 Manfrotto tripods.
Diane