I think we should add the HRE Emperor Frederick II. (1220 - 1250) as a ruling authority for Abbey Lindau. There are several coins were minted there in the time of King's participation on minting rights of the Abbey. Example:
Are we sure this is not just coins from the Royal mint of Lindau?
Königliche Münzstätte Lindau
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Are we sure this is not just coins from the Royal mint of Lindau?
Königliche Münzstätte Lindau
A legitimate question. Julius Cahn stated in his 1911 book that at the time of this bracteate, the right to mint coins in Lindau belonged solely to the king. It only passed to the (Women's) Abbey in 1272. Ulrich Klein has demonstrated in his more recent work that earlier Lindau pennies were minted by the abbey. From 1215 (until 1272) the king only participated on it. Ruitishauser also endorses this opinion in his standard work. It also seems plausible to me.
Yes those types should go in HRE like those and also check for duplicates poke @silvergeek
@Compendium : why do you think, the coin belongs to HRE? It is clearly a product of join minting of the abby (Linden branches) with support of the king (crowned head). This is not just my opinion but the result of modern research in this field.