First of all if you are able to stand you should pray while standing, else your prayer is void if there are no real and strong reasons (see also this hadith).
facing the qiblah is one of the conditions of prayer being valid, and
every worshipper should try to find out the direction of the qiblah
when praying, either by using natural signs or compasses, if possible,
or by asking trustworthy people in the place, who know the direction
of the qiblah. (see also here)
One can deviate a little bit some may say up to 180° to the qiblah based on this hadith narrated by ibn 'Omar, abu Huraira , 'Omar ibn al-Khattab and according to Imam at-Tirmidhi ibn 'Abbas and Ali ibn Abi Talib (May Allah be pleased with all of them):
“Whatever is between the east and the west is qiblah.”
Some scholars say this counts for Medinah only. But one could deviate from the Qiblah to an amount which maybe accepted as a form of "ijtihad" to find a qiblah...this means maybe arount 45° degrees left and right. Maybe even more, as:
Al-San’aani (may Allaah have mercy on him) said in Subul al-Salaam (1/260): This hadeeth indicates that it is obligatory to face the direction of qiblah, and not the exact position of the Ka’bah for those who are not able to face it precisely. End quote (same source as before).
Read also this fatwa in Arabic on the significant amount of deviation according to this hadith.
But in your case you seem to know that you are deviating from the qiblah and don't deviate by fault or due to uncertainty after a certain ijtihad.
So maybe a walk around could be, starting your prayer in the direction of the qiblah or the most possible direction you could deviate from and pray in the direction you mentioned as this was for example told some Pilots in this fatwa of the Saudia-Arabian fatwa council (Questions 27-29), as at least this was the case for our Messenger when he prayed on his horse or camel according to this hadith which you might also find in Musnad Ahmad. But note that this fatwa or hadith is dealing with an other situation. But as stated in the comments sometimes a necessity might allow you to perform things which are not allowed.
Here an other reference on the situation where one may not pray facing the qiblah.