was there a better line to play here?

Rapid game that was won on time. I did not like the Kf7 move but did not want to lose the e6 square. In the end, I exchanged the Queen for the two Rooks and this should have been a draw were it not for White being down to 50 sec. Could I have played differently without risking the loss of the pawn at e6? [Event "srymk72s vs. playchessordie19"] [Site "Chess.com"] [Date "2025-02-16"] [White "srymk72s"] [Black "playchessordie19"] [Result "0-1"] [WhiteElo "1513"] [BlackElo "1637"] [TimeControl "600"] [Termination "playchessordie19 won on time"] 1. d4 d5 2. Nc3 e6 3. Bf4 c5 4. e3 Nc6 5. Bb5 Qb6 6. Bxc6+ bxc6 7. Rb1 cxd4 8. exd4 Bb4 9. Ne2 Qd8 10. a3 Ba5 11. b4 Bc7 12. Bxc7 Qxc7 13. O-O Nf6 14. h3 Ba6 15. Re1 O-O 16. Ng3 Bc4 17. Nh5 Nxh5 18. Qxh5 g6 19. Qh6 Qe7 20. Nd1 Qf6 21. Ne3 Qxd4 22. Rbd1 Qg7 23. Qf4 Ba6 24. Ng4 f5 25. Ne5 Bb7 26. Nd3 Rae8 27. Qd6 Qe7 28. Qe5 Rf6 29. Re2 Ba6 30. Re3 Bxd3 31. Rdxd3 Kf7 32. h4 f4 33. Rf3 Rf5 34. Qe2 Qxh4 35. Rh3 Qf6 36. Rxh7+ Kg8 37. Rdh3 Qa1+ 38. Kh2 Qf6 39. Qa6 f3 40. Qxc6 Qe5+ 41. g3 Ref8 42. Rh8+ Qxh8 43. Rxh8+ Kxh8 44. Qxe6 Re8 45. Qxg6 Ree5 46. Qh6+ Kg8 47. g4 Rg5 48. Kh3 Rg7 49. Qa6 Re2 50. Qc8+ Kf7 51. Qf5+ Kg8 52. Qxd5+ Rf7 53. Qg5+ Kf8 54. Qh6+ Ke7 55. Qg5+ Rf6 56. Qg7+ Ke6 57. Qg5 Rxf2 58. Qe3+ Kf7 59. Qxf2 Kg6 60. Qg3 Kg7 0-1