Thanks for your prompt attention.
Why is the aspect of Shemittoh for Hadassim not raised by the Gemorah which talks about Esrogim. Having several blatt earlier explained why it is permitted to smell Esrogim growing on a tree and not Hadassim, that the element of 'smelling' is more appropriate to Hadassim and therefore the gezeroh of breaking off a branch applies. Considering that flowers do have Kedushas Shevi'is the Gemorah should have raised this query.
RASHI 39a DH NOSEN writes that he bought the entire Hoshanah i.e. the Lulav, Hadasim and Aravos all together. So the Mishnah does in fact mention Hadasim. See also RASHI 37b DH HO'IL who writes that the whole bundle is referred to as "Lulav". Presumably in the same way as Gemara 39b says that the Lulav referred to in the Mishnah grew in the sixth year and therefore does not possess Kedushas Shevi'is, so also the Hadasim grew in the sixth year and do not possess Kedushas Shevi'is. See also MELECHES SHLOMO on the Mishnah who writes that the word "Lulav" includes all 4 species.
(Our text of Gemara Sukah 37b that you cited is the opposite to what you wrote. One is allowed to smell Hadasim attached to the ground on Shabbos because they are used for smelling, so there would be no need to pluck them off on Shabbos. However, one may not smell an Esrog on its tree on Shabbos because an Esrog's chief purpose is for eating and therefore through smelling it one might come to pick it off. However, your text seems appropriate to what GILAYON HA'SHAS cites there.)
KOL TUV
D. Bloom
Here is another explanation why the Gemara does not mention Hadasim. It is simply because Lulavim cost more than Hadasim. The Gemara cites a Beraisa that one may not hand over to an "Am ha'Aretz" money from Shevi'is produce which is worth more than the value of 3 meals. TOSFOS DH YOSER writes that a Kosher Esrog, which is beautiful and that one can make a Berachah on, is expensive and worth more than the value of 3 meals. If it would have been worth less than this there would have been no problem about buying it from the Am ha'Aretz. Similarly one can say that a Kosher Lulav is also expensive. In fact MEIRI DH VEHA'MISHNAH writes explicitly that both the Esrog and Lulav are expensive. Therefore the only reason there is no problem buying the Lulav in the Shemitah year is because the Mishnah refers to a Lulav of the 6th year, as Gemara (below 39b) states.
In contrast, it seems from the Gemara above (34b) that Hadasim were cheaper. The Gemara there reports Shmuel as warning the Hadasim sellers that if they did not keep their prices reasonable, he would rule according to R. Tarfon, who was more lenient, and this would make Kosher Hadasim more plentiful and would lower the price. This suggests that Chazal had more power over the prices of Hadasim than over the prices of Esrog and Lulav. RABEINU CHANANEL there explains that Shmuel told the vendors to sell their Hadasim cheap.
Therefore the Mishnah did not mention Hadasim because their value is less than the worth of 3 meals, and there would not normally be any problem buying them from an Am ha'Aretz during the Shemitah year. According to this there is no proof from the fact that the Mishnah omitted Hadasim that Kedushas Shevi'is does not apply to them.
(It may be that the reason why people were prepared to pay more for the Lulav is because it is the principal one of the 4 species and therefore the Berachah is "Al Netilas Lulav", since it is the tallest of all the species - see Gemara above (37b) and RASHI there DH HO'EEL)
KOL TUV
D. Bloom