That's why I said loosely based.

The "R" was what I used for most of my search, but overall Goudy seemed like a decently good fit... and that "J" looks like it may indeed be a custom addition. There are a few fonts out there that match your "R" better than Goudy's, but the rest of the fonts were so far off that I didn't bother linking them.

<font class="dontLookLikeCrap">Closest I found was Criterion Medium:

http://www.myfonts.com/fonts/urw/criterion/urw-t-medium/</font>

The R is different but at lease it is close.

This sign comes out of the sign-painting tradition, not the world of type. Although there are cross-influences between the two disiplines (and in fact they have completely and sadly merged in the last few decades), any similarity to an existing font with something as old as this seems to be would be a happy coincidence.

Something like Beaufort would give a similar overall look, even though the J and R are different.

Sorry, I think neither of those is as close as Mark's suggestion (Beaufort). Perhaps you are letting the J influence you too much. Your best chance would be to see if you could blend a closer J and R with the right weight of Beaufort.

The fact is that you are looking for something that probably doesn't exist, as Mark explained, so the best you can do is come as close as possible, or pick a completely new direction, so that it just doesn't doesn't look like a poor match, but a conscious choice for a different look.