this sutta is quite instructive on kaaya and citta and mano and sukha.
a few highlights:
SN 51.22 ayoguḷa-suttaṃ
SN 51.22 iron-ball-discourse
(can mind made body travel to brahma world?)
“abhi-jānāti nu kho, bhante,
"[by means of] direct-experience, Lord,
bhagavā iddhiyā
(has) the-Blessed-One (using) [spiritual]-power
mano-mayena kāyena
(with a) mind-made body
brahma-lokaṃ upasaṅkamitā”ti?
{traveled to the} brahma-world?
“abhi-jānāmi khv-āhaṃ, ānanda,
“(through) {my own} direct-experience, Ānanda,
iddhiyā mano-mayena kāyena
(using) [spiritual]-power (of a) mind-made body,
brahma-lokaṃ upasaṅkamitā”ti.
(to the) brahma-world (I’ve) traveled.”
(can anatomical body travel to brahma world?)
“abhijānāti pana, bhante,
"{What about,} direct-experience, Lord,
bhagavā iminā cātu-mahā-bhūtikena
******* (of) these four-great-elements
kāyena iddhiyā
[making up the] body, (with) spiritual-power
brahma-lokaṃ upasaṅkamitā”ti?
[have you] {traveled to the} brahma-world?
“abhijānāmi khvāhaṃ, ānanda,
“(through) {my own} direct-experience, Ānanda,
iminā cātu-mahā-bhūtikena
(with) these four-great-elements
kāyena iddhiyā
[making up the] body, (with) spiritual-power
brahma-lokaṃ upasaṅkamitā”ti.
(to the) brahma-world (I’ve) traveled.”
this sutta serves as a commentary for how the standard formula for supernormal powers in 6ab, explicitly stated a couple of times, with the part of interest,
so an-eka-vihitaṃ
He {experiences} many-types
iddhi-vidhaṃ pacc-anu-bhoti —
(of) various-[spiritual]-powers *** ** ****-
eko-pi hutvā bahudhā hoti,
one (he) has-been, many (he) becomes,
bahudhā-pi hutvā eko hoti …
many (he) has-been, one (he) becomes …
pe …
…
yāva brahma-lokāpi
as-far-as (the) brahma-world
kāyena vasaṃ vatteti.
(with his) body, mastery (he) exercises.
and the mind and body dichotomy used in the similes and the meditation instructions themselves to do the levitation,
samaye tathāgato
when (the) Tathāgata’s
kāyampi citte samodahati,
body {is immersed} in-the-mind,
cittampi kāye samodahati,
(and) mind {is immersed} in-the-body,
sukha-saññañca
pleasurable-perceptions
lahu-saññañca kāye
(and) light-weight-perceptions (in regard to the) body
okkamitvā viharati;
(he has) entered (and) dwells (in);
tasmiṃ, ānanda,
******, *******,
samaye tathāgatassa
(on that) occasion (the) Tathāgata’s
kāyo appa-kasiren-eva
body (with) very-little-difficulty
pathaviyā vehāsaṃ abbhuggacchati,
(from the) earth (to the) sky (he) rises-up.
so some points i want to make, if it’s not very obvious from the passages quoted, is when we see mind and body being contrasted in suttas related to samadhi, body is so often referring to the anatomical body made of 4 great elements, as this sutta makes explicit.
when we see “kāyena” used in , i don’t have to dig up a pali grammar book to check if it’s a polynomial or abdominal 
yāva brahma-lokāpi
as-far-as (the) brahma-world
kāyena vasaṃ vatteti.
it’s talking about a flesh and blood body made of 4 elements.
when the buddha talks about
kāyampi citte samodahati,
body {is immersed} in-the-mind,
cittampi kāye samodahati,
(and) mind {is immersed} in-the-body,
sukha-saññañca
pleasurable-perceptions
putting aside whether sukha is a mental, physical, or both, the fact that a meditator who needs 4th jhana or higher samadhi to be able to perform this feat (of levitation), is it so hard to imagine sukha + kāyena from 3rd jhana standard formula referring to a flesh and blood anatomical body that experiences sukha?