I tried using site search to find every instance of yantra in the Valmiki Ramayana to see if this has any merit:
Every verse mentioning Yantra in Valmiki Ramayana:
atha bhuumi pradeshaGYaaH suutra karma vishaaradaaH |
sva karma abhirataaH shuuraaH khanakaa yantrakaaH tathaa || 2-80-1
karma antikaaH sthapatayaH puruShaa yantra kovidaaH |
tathaa vardhakayaH caiva maargiNo vR^ikSha takShakaaH || 2-80-2
kuupa kaaraaH sudhaa kaaraa va.nsha karma kR^itaH tathaa |
samarthaa ye ca draShTaaraH purataH te pratasthire || 2-80-3
1; 2; 3. atha = then; bhuumipradeshajJNaH = those able to advise on the nature of soils; suutrakarmavishaaradaaH = those skilled in thread-holding for levelling purposes; shuuraaH = those who were energetic; courageous; svakarmaabhirataaH = interested in doing their own jobs; khanakaaH = excavators; tathaa = and yantrakaaH = mechanics; karmaantikaaH = labourers; sthapatayaH = engineers; puruSaaH = men; yantrakovidaaH = skilled in machines; tathaa = and vaardhakayaH = carpenters; margiNaH = road- menders; vR^ikshatakSakaaH = wood-cutters; kuupakaaraaH = hallow-makers; sudhaakaaraaH = men skilled in plastering and white washing; tathaa = and vamshacharma kR^itaH = basket-makers and tanner; yet = those who; samarthaaH = were skilled; draSTaaraH = supervisors; pratasthire = sallied forth; purataH = in advance.
Then, those able to advise on the nature of soils, those skilled in thread-holding for leveling purposes, those who were energetic courageous and attentive in doing their jobs, excavators, mechanics, labourers, carpenters, road-menders, wood-cutters, hollow-makers, men skilled in plastering and white washing, basket makers, tanners and skilled supervisors of work sallied forth in advance.
हरि वागुरया व्याप्तम् तप्त कांचन तोरणाम् || ४-१४-५
प्राप्ताः स्म ध्वज यंत्र आढ्याम् किष्किन्धाम् वालिनः पुरीम् |
5b, 6a. hari vaagurayaa vyaaptaam = monkey's, by snares, she who is spread out [Kishkindha]; tapta kaancana toraNaam = burnt [purified] golden, [decorated with] having arch-ways; dhvaja yantra aaDhyaam = flags, machinery, impregnated with; vaalinaH puriim kiSkindhaam praaptaaH sma = Vali's, city, at Kishkindha, arrived, we are.
" She whose arch-way is decorated in gold, who is spread out with snares of monkeys, and who is impregnated with flags and machinery, we arrived at such city of Vali, Kishkindha. [4-14-5b, 6a]
kavaaTatoraNavatiiM suvibhaktaantaraapaNaam |
sarvayantraayudhavatiimu petaaM sarvashilpibhiH || 1-5-10
- kavaaTa toraNa vatiim = (she [city of Ayodhya] had) gateways with triumphal arches, [arc de triomphe], suvibhakta antaraapaNaam = shops with well laid out interiors, sarva yantra aayudha vatiim = she had all the required weapons and machinery, upetaam = consisted of, sarva shilpibhiH = all kinds of craftsmen.
That capital city Ayodhya had arched gateways with splendid doors. She had markets with well laid out interiors. She also had all required weaponry and machinery, along with various craftsmen such as artisans, artists and sculptors etc
sa tu dR^iShTvaa rudan diinaH papaata dharaNii tale || 2-77-9
utthaapyamaanaH shakrasya yantra dhvajaiva cyutaH |
- diinaH = miserable as he was; dR^IshhTvaa = to see; (the spot); saH tu = that Bharata; papaata = fell; rudan = weeping; dharaNiitale = on the ground; yantradhvajaH iva = as a flagstaff fastened by any mechanical contrivance; chyutaH = would drop; utthaapyamaanaH = while being raised; shakrasya = in honor of Indra the god of celestials.
Miserable as he was to see the spot, Bharata fell weeping on the ground, as a flag staff fastened by any mechanical contrivance would drop down while being raised in honor of Indra the god of celestials.
tām ratna pūrṇām bahu samvidhānām |
prāsāda mālābhir alamkṛtām ca |
purīm mahā yantra kavāṭa mukhyām |
dadarśa rāmo mahatā balena || 6-39-29
- raamaH = Rama; mahataa balena = with the great army; dadarsha = saw; taam = that; puriim = city; ratna puurNaam = full of precious gems; bahusamvidhaanaam = having various kinds of facilities; alamkR^itaamcha = adorned with; praasaada maalaabhiH = rows of mansions; mayaayantrakavaaTa = mukhyaam = having excellent doors with huge mechanical appliances; mahataa = and with a large; balena = armed forces (protecting the city)
Rama with his great army saw that City, full of precious gems, having all kinds of facilities, adorned with rows of mansions, having excellent doors with huge mechanical appliances and with a large armed forces protecting the City.
Thus, I have no idea where even the idea that Kumbhakarna was a Yantra comes from. Although apparently huge mechanical doors are a thing in Rāmāyaṇa, so there is advanced technology.