Utilizing both TTL and RS-232 level signals from transceiver
That's what happens when you rely on undocumented behavior.
Unless I'm misinterpreting your question, you seem to expect to be able to override the xxx213 logic outputs while they are enabled ...
Why do you expect to be able to do this?
The behavior you're seeing indicates that the SP213's logic outputs are better able to source current to drive a high level output than the MAX213's are.
The datasheets for these parts don't seem to give a spec for how much current they can source on these pins so your 'off-label' usage is difficult to predict - but really the results you're seeing are unsurprising.
You've just been lucky with the MAX parts up to now, but if Maxim made an internal change to the IC for whatever reason you could end up stuck with the same problem even with these parts.