Insuring at less than "full value" can happen in 2 ways--one I'd worry about, the other, not. We also have Boat US coverage on our 41 year old Rawson 30. But, that boat's worth next-to-nothing so it doesn't matter. On the larger boat, we're not eligible for a regular policy til she's ready for launch, right now she's only eligible for the construction policies. Having said all that....
If you're under-insured because the insurer is only willing to give you "actual cash value" on damage, then that's a worry. Especially if you're paying for a regular policy but will only get cash value because of the age of the components, etc. Actual cash value policies are supposed to be cheaper than regular policies. If you're worried about being under-insured because the insurer won't insure you for the full market value of the boat (i.e. they'll write a 100K policy but you can see on Yacht World that boats similar to yours are selling for 170K on average) that isn't such a huge problem--losses tend not to be the whole boat, it tends to be repair/replace part of the boat's value and if at real replacement instead of some kind of depreciated cash value, then its probably ok. Further, you're not paying for something you're never going to get!
I know I'm a little worried about the value the surveyor is going to put on our boat when we're done because its going to be more money than I'm willing to insure the boat for. I don't like paying for insurance that I think I'm not going to need. We're not counting our "sweat equity" so our cost of rebuilding the boat is quite a bit less than it would be if we have to hire someone to do everything.
Of course, I kinda wonder about the "actual cash value" policies and boats as that are anything over 40 years old or so--I have more than fifty large Merriman blocks in good working condition that I've seen fetch more at swap meets than brand new reproduction Merriman-style wood blocks. Same goes for much of the bronze on the boat. On something "new" actual cash value can be dismal because I'll assume the insurer is looking at depreciation down to something you'd buy at the marine swap meet. On something "old" like the blocks and winches we're rebuilding, actual cash value can be high (same marine swap meet)--if we're talking apples to apples and things that work well and aren't worn out, that is.
Other related thought...
I haven't investigated the matter fully, but it is possible to get a new build-date (and new CG Doc #) on a boat that has been extensively rebuilt. We're not planning on doing it because our cruising boat has been continuously CG documented since it was launched in 1931, but some folks do it for insurance reasons. Clearly, a 2007 build date sounds a lot better to the average insurer! Our surveyor states there's no hard-and-fast rule on it, but he figures about 25% of the structure must be repaired/replaced (on a wood boat like ours that would be planking, deck, frames, floors, keelbolts, etc.) which we've exceeded. I also don't really know what it takes to get the new CG Doc #. One would assume that all the system and hull safety standards that may be required are the same as those we strive to meet anyway! You may investigate this if you feel you've rebuilt your boat sufficiently to qualify for a new build date.
About Lloyds--they must be ok, I know several folks who have cruised with Lloyds insurance. However, the people I know best who have Lloyds always have to take on extra crew to be insured while crossing oceans. They never have a problem finding volunteers since they have a great boat and everyone wants to sail it! They are a couple who can handle their 50' schooner just fine--he's owned and sailed the boat for a few decades. But, their insurance will only cover if they've got 4 people on board for passage making. I do believe that makes sense, but you might not like finding yourself constrained to having to have crew for bluewater coverage. I know another owner of a 48' boat with similar requirement. He did the Transpac a couple years ago--his racing crew flew home and he then had to get additional crew for the trip back to the CONUS.
How big is your boat? Will this likely be an issue for you?
Good luck in finding an insurer that you like. You may check out the brokerage http://www.overseainsurance.com
they represent many different carriers.