Yeah, you shouldn't compare it to the barbarian because while the mechanics are similar looking they function differently. This is almost a RAW/RAI problem (I say almost because you're taking the ruling for changing the ability scores of a character and applying it in this situation (when the eidolon and the PC are two separate characters.)
If a barbarian rages, or a mind flayer eats your brains or any number of other status effects that change your ability modifier, certain scores can go up or down. For example, when you begin a rage a barbarian's Con mod does go up, and this gives the barbarian extra hitpoints that last for however many rages the barbarian uses. Conversely, when a mind flayer or other monster lowers your int score you can lose feats, skills and other abilities.
That rule only affects things happening to a single character. The Synthesist doesn't change her Con score, she only substitutes it. The rules specifically states that you use the eidolon's con score, but your hitpoints remain the same (you don't gain or lose hitpoints, only temporary hitpoints equal to the eidolon's hp.) Now, you can technically use the eidolon's con mod for skill rolls involving constitution, and any special attacks that raise or lower constitution would raise or lower the eidolon's score (for example, if the eidolon somehow had a barbarian's rage that would raise your temporary hp for as long as the eidolon is raging), but you can't gain or lose hp because of your eidolon's con score.
Slams actually do the same as punches if you spec it right. A monk's robe raises your AC bonus and your punch to 1d8 (the same as slam), you also get to flurry with full BAB and extra attacks from having a BAB over 5. Slam is a natural attack and thus limited to the max number of natural attacks you can make, and the math for primary and secondary attacks never really looked all that worth it in the long run when I could equip weapons of varying elements and materials to add to my basic flurry. And -1/-1 plus full Str mod (not counting power attacks) isn't as limiting as 0/0 +1/2str mod for a slam with secondary attacks.
Furthermore it was ruled that unless you're specifically using those special monster accouterments (claws/wings/tails/etc) the monk's stunning fist and other feats will work. The monk's body is treated as a weapon that can do lethal, but a monster with monk levels can't use its natural attacks for the monk's powers, but it can use basic unarmed, similarly a monster with a sword can use a power attack or other combat feats so long as it's only with the sword. So you can punch with the monster, and it'll use your Wis mod for the monk powers and it's Str mod, but you can't add natural attacks or anything to that.
Math-wise, using the primary/secondary attacks probably evens out and gets better later on, but with the monk the cost is 1 evolution point (for going full-summoner) compared to flurry, stunning fist, bonus feat, unarmed strike and the bonuses to AC you get while wearing no armor. As a synthesist all your physical stats are dump stats except Con which can be "alright", and the monster doesn't need any mental stats whatsoever. So you're free to pump up Cha +4, Con +2 and Wis +2 (with Int, if you really want to, but it can remain semi-low) and be on top.
And again, if I wanted to make a big crushing monster I'd go all synthesist and make a broken monster with a million arms like everybody else. The goal here is to make a character that balances the Monk's MAD with the Synthesist's broken ability to cover a lot of stats.
