1. If Master did sign it both ways, why did SRF have to resort to a forged version of his signature, many years after his passing. One would think that in those years they could find a legitimate signature with the extra 'a'.
2. It's now been over fifty years since the Master's passing. SRF still hasn't produced a legitimate signature with the extra 'a'. By now, they will need to show the original, not a copy, because people don't trust them anymore.
By the way, there are hundreds of copies of the Master's signature without the inserted 'a'. I've seen several books signed by him- including two signed after 1950. Both were signed 'Paramhansa'. The burden of proof is surely on SRF by now. Let's see an original signature, analysed by a handwriting expert, with the extra 'a'.
You can see some of these signed books at the Ananda Shrine of the Masters- where there are many holy relics, such as Sri Yukteswar's cane (the one he was holding in the well known picture of the two Gurus standing together).