Establish more secure symmetric crypto system given A and B have small initial secret
My understanding is $x$ or $g^{atx} \bmod p$ or $g^{btx} \bmod p$ would be expensive to find for Trudy, thus Alice and Bob retain confidentiality.


Not really.  Trudy knows $g^a$ (Alice sent that) and $t$ (Trudy picked that); let us assume that Alice uses the value $g^{atx} \bmod p$ for something, such as deriving symmetric keys, and then uses that to encrypt a message.  What Trudy could do it compute $(g^a)^{tx} \bmod p$, for all possible values of $x$, and derive keys from all of them; that's 16384 possible keys.  Trudy can then try to decrypt Alice's message using each key; the one that works will tell her the correct value of $x$ (and then she can either continue with a MITM attack, or impersonate Bob).

There are protocols that don't have this weakness, examples include EKE and SRP; these don't prevent Trudy from taking a random guess of $x$, attempting a MITM attack (and learning whether that was the $x$ that Alice and Bob shared); what they do is make sure that Trudy can't do any better; to test 1000 possible $x$ values, she'll need to perform the MITM attack 1000 times.