The historical core meaning of the word "idiot" was a person with a low IQ to a developmentally disabled degree
This is not so.
The other, which I think is a more recent restrictive sense and probably derived from the first restrictive sense, refers more specifically in some contexts to someone who is is oblivious to their own romantic feelings or to the romantic feelings of someone (usually a friend) who is in love with them.
I find this remarkable. Do you have some support for this?
The earliest entry in the OED shows that an idiot was merely someone who was generally ignorant, either by circumstance, or a lack of specialised learning:
A. n. 1.a. A person without learning; an ignorant, uneducated person; a simple or ordinary person. Now archaic and rare. [With reference to the Apostles (see quots. c1384, c1450) ultimately after ancient Greek ἰδιώτης in its specific sense ‘ignorant, layman’(so in Acts 4:13, the passage translated in quot. c1384).]
c1384 Bible (Wycliffite, E.V.) (Douce 369(2)) (1850) Deeds iv. 13 Forsoth thei seynge the stedfastnesse of Petre and John, founden that thei weren men with oute lettris, and idiotis
[a1425 L.V. men vnlettrid, and lewid men; L. homines..sine litteris et idiotæ], wondriden.
We can see a weakening and specialisation of the word a very short while later:
b. †(a) A person without professional training or skill (obsolete); (b) a private (as opposed to a public) person, an inward-looking person (now rare).
a1400 tr. Lanfranc Sci. Cirurgie (Ashm.) (1894) 69 (MED) But þe modir of þat child sente for a lewde leche [L. layco]..Þanne a fisician..blamede þe modir & hir freendis þat þei hadden left counseil for þilke idiotis biheeste.
These meaning (informed by context) lasted until the late 17th/early 18th century. (There is a 20th century example but we need not bother with this.)
However, it did not take long for “idiot” to become a classification at law and medicine.
2.a. Chiefly Law and Psychiatry. A person so profoundly disabled in mental function or intellect as to be incapable of ordinary acts of reasoning or rational conduct; spec. a person permanently so affected, as distinguished from one with a temporary severe mental illness. Now historical in technical use.By the older legal authorities in England an idiot was defined as a person congenitally deficient in reasoning powers (cf. quot. 1590), and this remained for a long time the common implication of the term.
c1425 Bk. Found. St. Bartholomew's (1923) 13 (MED) He made and feyned hym-self vnwyse..and owtward pretendid the cheyr of an ydiotte.
1590 H. Swinburne Briefe Treat. Test. & Willes ii. f. 39 An Idiote, or a naturall foole is he, who notwithstanding he bee of lawfull age, yet he is so witlesse, that hee can not number to twentie, nor can tell what age he is of, nor knoweth who is his father, or mother, nor is able to answer to any such easie question.
The 1590 quote is significant as it marks a milestone in the treatment of the mentally disadvantaged, and separates those of low IQ and those who were mentally ill.
The 1774 Madhouse Act did not mention idiots, it referred to “lunatics”, which included anyone who wasn’t in their right mind for any reason.
The 1833 Chancery Lunatics Act did expand the categories
"An Act to diminish the inconvenience and expense of Commissions in the Nature of Writs De Lunatico inquirendo; and to provide for the better care and treatment of idiots, lunatics, and persons of unsound mind found such by inquisition".
These terms were then formal terms.
This legal/medical meaning of “Idiot” was superseded by other terms (Educationally Subnormal, Subnormal, and Severely Subnormal) in the UK under the Mental Health Act 1959, and the use of “idiot” as a category was thereby ended.
Finally we have the chief current meaning:
2 b. A person who speaks or acts in what the speaker considers an irrational way, or with extreme stupidity or foolishness.
c1480 (▸a1400) St. Theodora 148 in W. M. Metcalfe Legends Saints Sc. Dial. (1896) II. 103 Wenand I ware sic a ydiot, þat þu suld wit my priuete.
2002 J. Thompson Wide Blue Yonder ii. 121 Now she'd ruined everything by being an idiot.
From the above, and in broad terms, we can see that “Idiot” started off in the 14th century as meaning “the ordinary people”, and although this lasted until the 17th/18th century (but seems to have diminished in use as time went on) almost immediately "idiot" took on the meaning of someone who acted in a stupid manner at any time.
The meaning of “a stupid person/ a “fool” had been there since more or less the introduction of the word in the 14th century, and this has become the popular, and only current meaning.
(1) when did these more restrictive senses of the word "idiot" emerge, respectively, and when did they become more common than the now dated sense of the word?
The medical and legal categorisation of the mentally feeble, as “idiots” seem to have started, at least in the UK, in the late 16th century, and was formalised by the the 1833 Chancery Lunatics Act when Mental Health started to come to the fore (for various reasons). The categorisation then continued until 1959.
(2) is there a word for the process of a secondary meaning of a word becoming a more common way that a word is used than its original and core meaning?
I suppose it is a transition or evolution but this does not apply to the word “idiot” where, to all intents and purposes, the meanings have run parallel.