diff --git a/OemLoader/MainWindow.cs b/OemLoader/MainWindow.cs
index c82c2a8..ef3d125 100644
--- a/OemLoader/MainWindow.cs
+++ b/OemLoader/MainWindow.cs
@@ -52,13 +52,21 @@ public class MainWindow(string title)
             orb = Orbit.CreateFromStateCci(childCelestial, simTime, newPosition, newVelocity, orb.OrbitLineColor);
         }
         
-        // Go to the specified time and set the vehicle's orbit to the ephemeris orbit at that time
-        // (this even works backwards in time, thanks to the patch in UniversePatch!)
+        // Go to the specified time (thanks to UniversePatch.ApplyVehicleSolversTranspiler this works
+        // even for negative values of dt)
         var dt = simTime.Seconds() - Universe.GetElapsedSeconds();
-        Universe.CompleteAndApplyPreviousOrbitSolvers();
+        // This is similar to the implementation of the stock `simulate` console command, but we
+        // reset the simulation speed to 1x to avoid the bug in that command where the time step
+        // gets multiplied by the simulation speed
+        var step = Universe.GetJobSimStep(dt);
+        Universe.ApplyVehicleSolvers();
+        Universe.ApplyOrbitSolvers();
         Universe.ResetSimulationSpeed();
-        Universe.ExecuteNextOrbitSolvers(dt);
-        Universe.CompleteAndApplyPreviousOrbitSolvers();
+        Universe.ExecuteNextOrbitSolvers(dt, step);
+        Universe.ExecuteNextVehicleSolvers(dt, step);
+        Universe.ApplyVehicleSolvers();
+        Universe.ApplyOrbitSolvers();
+        // Finally, teleport the vehicle onto the orbit calculated from the ephemeris
         Program.ControlledVehicle.Teleport(orb, null, null);
         Log.Debug($"OemLoader: Jumped to time {time} from ephemeris");
     }
diff --git a/OemLoader/OemLoader.cs b/OemLoader/OemLoader.cs
index d4e7f30..f72870e 100644
--- a/OemLoader/OemLoader.cs
+++ b/OemLoader/OemLoader.cs
@@ -1,6 +1,5 @@
 using System.Diagnostics;
 using System.Reflection;
-using Brutal.Numerics;
 using HarmonyLib;
 using JetBrains.Annotations;
 using KSA;
@@ -46,13 +45,6 @@ public class OemLoader
         Log.Info($"OemLoader {Version} loaded");
     }
 
-    [UsedImplicitly]
-    [StarMapAfterGui]
-    public void AfterGui(double dt)
-    {
-        Window.Render();
-    }
-
     [UsedImplicitly]
     [StarMapAllModsLoaded]
     public void FullyLoaded()
diff --git a/OemLoader/ProgramPatch.cs b/OemLoader/ProgramPatch.cs
index ed3fe01..67e6391 100644
--- a/OemLoader/ProgramPatch.cs
+++ b/OemLoader/ProgramPatch.cs
@@ -1,4 +1,3 @@
-using Brutal.Numerics;
 using HarmonyLib;
 using JetBrains.Annotations;
 using KSA;
@@ -17,4 +16,15 @@ internal static class ProgramPatch
     {
         return !OemLoader.Instance?.Window.Typing ?? true;
     }
+
+    // Since KSA build 4036 we need to draw our UI in the thread safe portion of the frame since we could be
+    // modifying vehicle state
+    // FIXME: when StarMap adds proper hooks into OnDrawUiThreadSafe, use that instead of this manual patch
+    [UsedImplicitly]
+    [HarmonyPatch("OnDrawUiThreadSafe")]
+    [HarmonyPostfix]
+    private static void AfterGuiThreadSafe()
+    {
+        OemLoader.Instance?.Window.Render();
+    }
 }
\ No newline at end of file
diff --git a/OemLoader/UniversePatch.cs b/OemLoader/UniversePatch.cs
index 88cb8c4..e106ffe 100644
--- a/OemLoader/UniversePatch.cs
+++ b/OemLoader/UniversePatch.cs
@@ -14,9 +14,9 @@ internal static class UniversePatch
     // Without this patch, Universe._achievedSpeedFraction will end up as a large negative value after attempting to
     // go backwards in time, and stuff will start breaking.
     [UsedImplicitly]
-    [HarmonyPatch(nameof(Universe.CompleteAndApplyPreviousOrbitSolvers))]
+    [HarmonyPatch(nameof(Universe.ApplyVehicleSolvers))]
     [HarmonyTranspiler]
-    private static IEnumerable<CodeInstruction> CompleteAndApplyPreviousOrbitSolversTranspiler(
+    private static IEnumerable<CodeInstruction> ApplyVehicleSolversTranspiler(
         IEnumerable<CodeInstruction> instructions)
     {
         var matcher = new CodeMatcher(instructions);