I think Original plan is good
Okay.
I'll just briefly outline both plans, in terms of how far I plan to take the respective Komnenos dynasties:
NOTE: There will be spoilers, BUT, bear in mind that I am constantly coming up with new ideas and what-ifs, and I didn't even finish my first TL, so what is written here is not set in stone.
Original plan (following a prophecy I just made up on the fly)
Andronikos I (1183-1184): Assassinated by men loyal to his son, Manuel II.
Manuel II 'the Just' (1184-1199): Eldest son of Andronikos I. Dies of old age.
Alexios III (1199-1203): Eldest son of Manuel II. Assassinated by agents of Michael Komnenos Doukas.
Michael VIII Komnenos Doukas (1203-1204): Overthrown and killed by Constantinoplitan mob.
David I 'the Copper-hand' (1204-1222): Second son of Manuel II. Dies of an infect wound.
Romanos V 'the Pious' (1222-1235): Eldest son of David I. Dies of natural causes.
Andronikos II (1235-1243): Middle son of David I. Killed in battle against the Mongols.
Stephen I (1243-1253): Youngest son of David I. Accidentally killed in a church fire.
John III '
Porphyrogennetos' (1253-1258): Eldest son of Stephen I. Poisoned by Stephen II.
Stephen II '
Pinkernes' (1258-1261): Youngest son of Stephen I. Deposed by Isaac Rallis-Raoul. Flees to Wallachia, killed by bandits.
New plan (more influenced by the OTL line of Emperors of Trebizond)
Andronikos I (1183-1184): Assassinated by men loyal to his son, Manuel II.
Manuel II 'the Just' (1184-1199): Eldest son of Andronikos I. Dies of old age.
Alexios III (1199-1223): Eldest son of Manuel II. Dies of old age or stress.
John III 'the Bloodthirsty' (1223-1230): Eldest son of Alexios III. Dies of either poison or gout.
Manuel III 'the Great' (1230-1263): Third son of Alexios III. Dies of old age.
Andronikos II (1263-1266): Eldest son of Manuel III. Dies of unknown causes (Similar to his OTL counterpart).
George (1266-1268): Middle son of Manuel III. Dies of exhaustion playing tzykanion.
John IV (1268-1273): Youngest son of Manuel III. Dies of an infected wound.
David (1273-1274): Youngest son of Alexios III. Dies of old age.
Michael VIII (1274): Only son of David. Reigns for a few months before abdicating in favour of his cousin, Alexios IV.
Alexios IV (1274-1297): Only son of John IV. Dies of tuberculosis.
Andronikos III (1297-1318): Eldest son of Alexios IV. Badly injured during a Mongol raid. Dies 'in his sleep'.
Manuel IV (1318): Only son of Andronikos III. Reigns for 8 months before being sidelined and blinded.
Basil III (1318-1323): Second son of John IV. Charged with treason and strangled with a bowstring.
Michael IX (1323-1335): Third son of John IV. Dies instantly during a revolt when a civilian throws a piece of debris and strikes him in the head.
Isaac II (1335-1340): Youngest son of John IV. Deposed by Michael X Angelos, a court official and lover of his sister. Commits suicide due to extreme guilt and to avoid humiliation and execution.