It seems to me that you can resolve the Sha'agas Arye's "kusha atzuma" based on the Shita Mekubetzet in B.M., which writes that when the gemara says that "tovas hana'ah aino mamon l'knos b'chalipin" it means that "even if you hold tovas hana'ah is mamon, it is not 'mamon chashuv' to be bought/sold via chalipin, and therefore the sugya follows either opnion of 'tovas hana'ah mamon' or 'aino mamon'" (rough translation). IOW, the gemara in B.M. is concerned with the general debate of tovas hana'ah mamon or not (which is what R' Eliezer and R' Yosi in Pesachim are arguing about), but is a seperate discussion about the scope of kinyanim - can a kinyan agav or a kinyan chalipin (which are lower levels of kinyanim) work on this "inferior" type of possession called "tovas hana'ah"? The Shita Mekebetzet writes that this is meduyak in the gemara - the gemara doesn't say "aino ma'amon v' aino niknais" but rather "aino mamom liknos" , meaning only with respect to kinyan is tovas hana'ah aino mamon.
The only missing step is if kinyanim don't work on tovas hanaah, how did R' Gamliel transfer his ma'aser? The Ktzos (who also discusses the Shita Mekubetzet and the entire sugya) addresses this issue in a long discussion (275:1), the punchline of which is that if the kinyan to the other party fails, the tovas hana'ah becomes hefker, and kinyan agav will work on hefker.