The OP states, “I re-studied Romans, especially Romans 10:13, and I have come to believe that conversion is instantaneous…” The idea of “instantaneous” can neither be supported nor ruled out from the aorist of ἐπικαλέσηται in Rom 10:13.
Romans 10:13 NKJ
For “whoever calls (ἐπικαλέσηται, Strong’s 1941, aorist subjunctive
middle) on the name of the LORD shall be saved (σωθήσεται, Strong’s
4982, future indicative passive)”
Rather than conveying the amount of time it takes to complete an action, the aorist regards an action or event as a whole.
Greek Verbs: Aorist Tense
The aorist is said to be "simple occurrence" or "summary occurrence",
without regard for the amount of time taken to accomplish the action.
This tense is also often referred to as the 'punctiliar' tense.
'Punctiliar' in this sense means 'viewed as a single, collective
whole,' a "one-point-in-time" action, although it may actually take
place over a period of time.
In Rom 10:13 ἐπικαλέσηται is part of a indefinite relative clause (“For whoever calls”) that functions as the subject to the main verb σωθήσεται (“shall be saved”). In this construction, the uncertainty that underlies the use of the subjunctive lies more with the person, reflected in the word “whoever,” than with the verb. Thus, while the verb ἐπικαλέσηται is in the subjunctive mood, it is commonly rendered with the indicative “calls.” (Indefinite Relative Clause).
Given the above discussion, the aorist of ἐπικαλέσηται in Rom 10:13 is understood to convey the simple fact of the action without addressing the exact time or duration. The sense of past time appears only in relation to the action of the main verb, σωθήσεται, which is in the future tense. The aorist of ἐπικαλέσηται in Rom 10:13 opens up a range of possibilities. Calling on the name of the Lord may be an act that is instantaneous or one that takes an entire lifetime to unfold and come to completion.