SQL Server geography.Intersects Yields Unexpected Results (arch shape)

Question

I've coupled ESRI's ArcGIS with SQL Server 2008 R2 in an attempt to allow users to search for geographical points using a polygon (with ArcGIS' drawing toolbar). I've run up against an issue that's not making any sense to me. It seems easiest to illustrate it visually:

1. I draw a rectangle along the top of the northern hemisphere and get results I wouldn't expect (I know there are more points up there):

2. I draw a smaller square within that rectangle and get the results I was expecting:

Can anyone explain why this might be happening and if there's some way around it? It seems like a SRID mismatch, but I'm using 4326 for ArcGIS and for SQL Server.

If I switch to using geometry instead of geography the rectangle works fine. I assume this is because geometry isn't taking into account the curvature of the earth, which isn't present on the flattened-out map. geometry has problems of its own though (my map wraps infinitely left/right, and so some of my polygons refer to points outside 180 degrees, which geometry doesn't seem to support).

For reference, here are the results in SQL Server:

For the rectangle:

For the square:

And UnitsSearchByLocation looks like this:

ALTER PROCEDURE [dbo].[proc_UnitsSearchByLocation]
    @polyText varchar(4096),
    @wkid int
AS
    declare @g geometry
    set @g = @polyText

    declare @poly geography

    begin try
        -- try the polygon as provided, although it has the potential
        -- to be oriented incorrectly
        set @poly = geography::STPolyFromText(@polyText, 4326)
        select * from Unit where Location.STIntersects(@poly) = 1
    end try
    begin catch
        -- assume the error was a result of the orientation being wrong
        -- and attempt to correct it
        declare @validPolyText varchar(4096)
        set @validPolyText = @g.MakeValid().STUnion(@g.STStartPoint()).ToString()
        set @poly = geography::STPolyFromText(@validPolyText, @wkid)
        select * from Unit where Location.STIntersects(@poly) = 1
    end catch
GO

Although it seems irrelevant to me, I'm using this Imagery from ESRI (: - https://server.arcgisonline.com/ArcGIS/rest/services/ESRI_Imagery_World_2D/MapServer

Thanks for any help you can provide..