Curtis wrote: “I need advice. I have lee helm”
I did a little bit of research and found a sail pan for one of the versions of Peep Hen.

I also found the we have two current members who have owned Peep Hens, (Shemaya L. and Glen M.), Glen having done a successful conversion to junk rig. You can contact them via the membership directory.
Hopefully you will get a reply soon to your lee helm concern. This one (Hedwig, owned at the time by Glen M.) appears to come up into the wind smartly, and sail away with what looks like very light weather helm in those conditions, or perhaps neutral, anyway, when he let the tiller go the boat did come up into the wind). Click here for the video.
It appears that Glen has put a junk rig onto the original mast, in the original mast position. Hopefully he will chime in and give more information.
I presume you are using the original mast position, and the original free-standing mast. I tried to transform the sail plan drawing into something matching your photo (which is not square on to the camera) in order to get some sort of comparison of the sail plans.

The result is not very satisfactory and photos are never any good for this, so if you can possibly do so, I suggest you post a proper drawing of your sail plan, so a proper comparison can be made. In theory, the geometric centre of your sail plan should be on the same vertical line as the geometric centre of the designed gaff rig sail plan. HOWEVER, that is only theory, and an eyeball of photos of other successful junk conversions suggests to me that you may have a little bit of leeway there – and the video clip of Hedwig shows that indeed a junk sail placed on the original mast can be successful on a Peep Hen.
It seems you have raked your mast aft a little, and slung the tack as far aft as you can, which ought to have helped a little in mitigating lee helm. Whether your sail can be slung even a little further aft by bringing the throat aft as well, as you suggest, I do not know as I don’t have experience with that type junk sail, but someone may be able to chime in on that possibility.
There might not be anything more you can do with that sail. You have one strike against you already, by opting for a flat sail, and it does seem that the geometric centre of your sail might still a little too far forward (IN THEORY) even after raking the mast and slinging the tack aft.
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Hedwig, referred to above, appears to be a junk sail on the original mast, which suggests to me that your conversion OUGHT to be OK, despite theory.
So, here are two important things you might like to consider, which are not to do with the sail, but everything to do with helm balance.
- 1. Shifting some weight so that your boat trims a little by the bow will usually help mitigate lee helm.
- My own little boat needs trimming by the bow in light airs. I find that just shifting my own weight to the forward end of the cockpit makes all the difference. Off the wind, I raise the board a little and shift my weight aft. When on the wind, in light airs, I have to put the board fully down and move my weight forward as far as I can.
- You might be able to shift some ballast, or your water tank, ground tackle or whatever, to trim by the bow a little.
- (In heavy conditions I don’t have lee helm. As the boat heels, weather helm begins to develop. You will find the same).
- 2. I found an interesting comment about the Peep Hen on the Wooden Boat forum: “Helped this guy launch his Peep Hen at the Richmond marina yesterday - nice! He said he'd modified the centerboard to be longer and much more foil-shaped, as the stock one performed poorly and didn't hang properly when fully down -- the single bolt didn't hold it well enough” (The link is here https://forum.woodenboat.com/forum/designs-plans/162825-/page2 )
Now, this is very important. If your centreboard is too short, or not going down fully, then you can expect to get lee helm. My little boat is very sensitive to that. When I bought my little boat and did the conversion, the first thing I found was excessive lee helm. I found it was caused by the centreboard not going fully down, and I had to attend to it. With the boat sitting on the trailer, it is impossible to ascertain if your centreboard is sticking and not going down fully. Out on the water, you won’t really know either. You might have to have to lift the boat on a sling, maybe hire a crane truck for a couple of hours, and check to see that the board is going down fully, or you might have to put the boat on the mud and haul it down by the masthead as I did with my little boat.
– but be careful doing that because your boat will have quite a lot of stability when sitting on the mud, and your tabernacle with the pin going through the mast (which is not a very robust detail) may not withstand careening in this way, nor the narrow tapered upper section of your mast. Maybe you can use jacks, and jack the boat up onto blocks. Anyway, unless you can be very sure that the board is going down all the way, that is what I would look at first. If the board is sticking when only 80% down, then I would expect you will have lee helm. While checking, make sure also that your centreboard is full length for the case. If it has been modified and shortened then that too could contribute to lee helm.
I hope Glen M will see this and comment from his direct experience with what appears to have been a successful conversion. That will be more valuable than my uninformed comments from the sideline.
If all else fails, you might have to put a little riding sail on the stern. But hopefully that won’t be necessary.
Regarding lowering the sail on Beau Peep, it would certainly look better. If it were mine, I would remove those cleats on the mast (which appear to be redundant) and rather than lowering the sail, I would add an extra lower panel, bringing the boom down as far as the halyard turning block - and make it cambered. That way you will learn that camber is just as easy to sew as flat, and you get a little bit of extra sail area that your boat will be able to carry with little or no loss of stiffness. Well, you did ask for comments...
(That Wooden Boat forum link, above, was of interest too, because it carries an anonymous post from 2014 by "WX" which looks suspiciously like Gary P.'s old Redwing. Am I right Gary?)