Good questions. 

My impressions are:

1) the flared end of a brasswind instrument does alter the pitch. And, I would suppose that a funnel shape would impact on it differently than would one that is flared.

2) the cylindrical nature of a garden hose would impact on several things including tone, pitch, harmonics, and stability of the note produced. 

3) I suspect that the mouthpiece will impact on range, as well as harmonics, but maybe less so than the remainder of the length of tubing and bell.

I think the Blow harder is getting it closer to where it should be.  And, you haven't gotten to the fundamental yet. If you cut off the fundamental you get F, Bb, D, F, Bb, C, D on say a trombone.    Count up one step from what you are getting and it is Eb= F, Ab = Bb, C = D, Eb = F, Ab = Bb, (skip),  C = D

So, I'm thinking you still have an Ab horn. 

With the very cylindric bore, a garden hose resembles a french horn. Most french horns are not able to play their own key note, which they are actually not intended to do.
That may confuse things because you may be an octave or a quarter (or more) out of tone compared to where you actually think you are on the tone scale.

I have some calculus on this site:
http://musikmuseum.dk/1SVING.HTM

The formulas given are the theoretic aspect. In practical experience, a brasswind instrument works as if the total tube length is sactually a little longer than what can be measured.
Measuring on the bell end is also not easy. On trombones and Sousaphones, the outer part of the belll is merely decorative. Cut it off, and the thing still plays in same tune...(but looks weird)

Bell shapes do vary, and there is (to my knowledge) no formula to calculate exactly where on the bell the borderline between "decorative" and "functional" goes, or how much extra air column needs adds on the actual tube length.

I have made instruments/frankenhorns or playing replicas of historic instruments, and yes the last adsjustment of the tubelenght is cut and try. I know the approximate lenght a given tuning requires, and what shape leadpipe, bell etc i want. But, the tuning slide is usually placed on a quite cylindrical part of the bore. So instead of the tuning slide, i use some piece of carden hose, that is adjusted until it is in tune. With the now measurable length of used gardenhose (minus the parts that go over the tube ends) i can not make the tuning slide to match.

It may sound unprofessional, but there is a vatiety of bells, from the almost zink-shaped to Sousaphone shaped, not to mention the special bells, like a whisper. Try to calculate that thing! I made a replacement for a lost whisper bell on a cornet with two bells, and was surprised how much different in lenght (longer) the whisper unit had to be compared to the normal bell, measured from the switch-valve. 

That being said, a tuning slide should always be pulled a little out for the instrument to be in tune.
In my view there is no use to have a lot of slide movement to give of, but nothign to take.

In my experience, instruments being a little off on the lower tones often suffer of some sort of being untight somewhere. That may be cracked tubes or ferrules, worn valves, broken cork in water key, damaged mouthpiece reciever (or mouthpiece shaft) just to mention some common reasons.

It is my understanding that each low note breaks free kind of,  from the bell at a different point.  The curvature of the flair seems very critical to the tuning of the low notes.  I would propose using a french horn bell and playing full range and gradually cutting off radius between playing to see how this effects what notes?

I have a Bb Alphorn made in Austria. While Conical in bore, its length should be about 9' or 108". The manufacturer says 275CM fully assembled.

The bell piece measures 59-1/8", the other piece measures 46-3/8", the mouthpiece protrudes 2-1/2". The total is 108" The joint that allows for tuning is 2."

That gives one an idea of the variation in length that allows for tuning based on player, mpc and environmental conditions, like temperature or altitude, etc.

The scale I am able to achieve is similar to the open tones of a Euphonium, Bb, F, Bb, D, F, G, Ab, Bb, C, D