I after my debugging, it turned out that my mistake was in the order of the scripts. Even though I was registering them all, I was not observing the correct order. This was the correct solution:
string telerikAssembly = typeof(RadScheduler).Assembly.FullName;
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Common.Core.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Common.jQuery.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Common.jQueryPlugins.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Common.TouchScrollExtender.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Common.Navigation.NavigationScripts.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.ComboBox.RadComboBoxScripts.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Common.Scrolling.ScrollingScripts.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Menu.RadMenuScripts.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Rating.RadRating.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Ajax.Ajax.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Splitter.RadSplitterScripts.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Splitter.RadSlidingZoneScripts.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Calendar.RadCalendarCommonScript.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Calendar.RadCalendarScript.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.PanelBar.RadPanelBarScripts.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Common.Popup.PopupScripts.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Input.TextBox.RadInputScript.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Input.DateInput.RadDateInputScript.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Input.NumericTextBox.RadNumericInputScript.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Calendar.RadTimeViewScripts.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Calendar.RadDatePicker.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Calendar.RadDateTimePickerScript.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.RadSchedulerScripts.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.ContextMenu.Plugin.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Views.Week.Model.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Views.Week.GroupedByResource.Model.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Views.Week.GroupedByDate.Model.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Views.MultiDay.Model.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Views.MultiDay.GroupedByResource.Model.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Views.MultiDay.GroupedByResource.Model.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Views.Day.Model.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Views.Day.GroupedByResource.Model.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Views.Month.Model.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Views.Month.GroupedByResource.Model.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Views.Month.GroupedByDate.Model.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Views.Timeline.Model.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Views.Timeline.GroupedByResource.Model.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Views.Timeline.GroupedByDate.Model.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Scheduling.AdvancedTemplate.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.Helpers.DateTime.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Scheduler.RecurrenceEditor.RecurrenceEditor.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Menu.ContextMenu.RadContextMenuScripts.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.Slider.RadSliderScripts.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.ToolBar.RadToolBarScripts.js", telerikAssembly));
scriptManager.Scripts.Add(new ScriptReference("Telerik.Web.UI.ListBox.RadListBoxScripts.js", telerikAssembly));
I guess I should point out that I got it working wothout the AjaxManager, but rather by putting everything in a RadAjaxPanel. I've had much better experiences with the panel in SP that with the ajax manager.