You're missing context in all of these verses-
First of all amisham has multiple meanings- it means meat but also pleasurable-enjoyable-royal things.
Lord rama promises that he will live like a common person disregarding his royal status like a hermit.
Let's look at the verses you have given-
"samaashvasa muhuurtam tu shakyam vastum iha tvayaa || 3-47-22
aagamiSyati me bhartaa vanyam aadaaya puSkalam | ruruun godhaan
varaahaan ca hatvaa aadaaya amiSaan bahu || 3-47-23
Be comfortable for a moment, here it is possible for you to make a
sojourn, and soon my husband will be coming on taking plentiful forest
produce, and on killing stags, mongooses, wild boars he fetches meat,
aplenty. [3-47-22b, 23]"
This is from aranya kanda, here Sita is talking with ravana in form of Brahmin. She is telling that her husband will come soon with "amesha" here amesha most likely means good food and not meat because offcource a Brahmin will not eat meat, the produce she is talking about is fruits. Why is it mentioned that ram kills animals? well for protection offcource.
The other verses are from ayodhya kand-
"aiNeyam maamsam aahR^itya shaalaam yakSyaamahe vayam | kartvyam
vaastushamanam saumitre cirajiivabhiH || 2-56-22
Oh, Lakshmana! Bring the meat of an antelope. We shall perform a
purifactory ceremony while entering the house. Which is to be done by
those who wish to live long.
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mR^igam hatvaa.a.anaya kshipram lakshmaNeha shubhekshaNa kartavyaH
shaastradR^iSTo hi vidhirdarmamanusmara || 2-56-23
Oh, large-eyed Lakshmana! Killing the antelope quickly, bring it here.
The prescribed rite according to scriptural point of view indeed is to
be performed. Keep in mind the sacred obligation.
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bhraaturvachana maajJNaaya lakshmaNaH paraviirahaa | cakaara sa
yathoktam ca tam raamaH punarabraviit || 2-56-24
Lakshmana the slayer of enemies, understanding his brother’s words,
acted as instructed. Rama spoke again to Lakshmana as follows.
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iNeyam shrapayasvaitachcchaalaam yakshyamahe vayam | tvarasaumya
muhuurto.ayam dhruvashcha divaso.apyayam || 2-56-25
Oh, gentle brother! Boil this antelope’s meat. We shall worship the
leaf-hut. This day and this instant also are of a distinctive
character. Be quick.
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sa lakSmaNaH kR^iSNa mR^igam hatvaa medhyam pataapavaan | atha cikSepa
saumitriH samiddhe jaata vedasi || 2-56-26
Then, Lakshmana the strong man and son of Sumitra, killing a holy back
antelope, tossed it in an ignited fire.
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tam tu pakvam samaaj~naaya niSTaptam chinna shoNitam | lakSmaNaH
puruSa vyaaghram atha raaghavam abraviit || 2-56-27
Feeling certain that it is cooked and heated thoroughly with no blood
remaining, Lakshmana spoke to Rama the lion among man as follows:
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ayam kR^iSNaH samaapta angaH shR^itaH kR^iSNa mR^igo yathaa | devataa
deva samkaasha yajasva kushalo hi asi || 2-56-28
This black antelope, with its complete limbs, has been cooked
completely by me. Oh, Rama resembling God! Worship the concerned
deity, as you are skilled in that act.
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raamaH snaatvaa tu niyataH guNavaan japya kovidaH |
samgraheNaakarotsarvaan mantran satraavasaanikaan || 2-56-29
Rama, the virtuous man and the learned man in chanting of sacred
spells, after taking bath and with subdued mind, briefly chanted all
the sacred scripts to be chanted at the end of a purifactory ceremony.
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iSTvaa devagaNaan sarvaan viveshaavasatham shuciH | babhuuva ca
manohlaado raamasyaamitatejasaH || 2-56-30
Worshipping all classes of deities and getting himself purified, Rama
entered the house. There was a heartful joy in rama, with his
limitless splendour."
These verses are once again taken out of context, It is clear from above verses that they did a purifactory rite and no meat was consumed as food I do not know if animal meat is used for any purifacatory rite?
does "aineyam mamasa" has any other meaning