My only fear with you getting a choke collar is that you don't have a history with the dog and while you are forming a bond YOU are not there in HER eyes yet. She MIGHT lash out if truly scared and then provoked. If it's that she is genuinely scared than it's because of you. She doesn't feel as if you can protect her (oddly enough) and are not in charge. Because of this she wants to flee to her SAFE ZONE (the house). I feel as if they read our emotions and then magnify them. You will have to be more assertive not with her but your surroundings. Just walk her as if you have been doing it all her life and there is nothing new or out of the ordinary about it. See you start of with treats which automatically raises her suspicions. These dogs are smarter than you think. Mine gets ice out of the ice maker and has figured out how to open doors. You bring treats near the door and they know whats next.

I would suggest spending more one on one time with her. Give her some love, message her, roll around with her (not that you don't already but do it just the two of you). While messaging her you could work out any dominance issues.

Think of it like this; if I suspect any dominance issues with me at all what I do is while doing the message (this is how I have done it with all my previous dogs and it works for me but might not for anyone else) I will work them into passive positions and then DOMINATE through message. PIN them down while rubbing pressure points. Throw a growl or two in for good measure. Before you know it they will be as submissive as you could of ever hoped for and she will TRUST YOU as you have shown here that you are in charge.

Something else you could try that I do is when we are alone and we hear something or something gets their attention don't automatically correct them. They are dog's and as such should act like dog's. I walk mine on a 6' leash so when she gets doggish she will pull all the slack on the leash (I walk her in a harness) and them FREEZE!!! While she is fixated I walk up behind her and will whisper something to the effect of "what's that" in a really inquisitive child like voice and she will explode with energy (well for a mastiff that means Bark once or twice and wag tail vigorously all the while keeping the least as taught as she could without me having to correct. She actually monitors the pressure on some level. These dogs are SMART). All this time I scan what she is fixated on. I only do this is nothing is there (like a leaf fell and made some noise that spooked her). I let her ACT LIKE A DOG and then bring her over (much as you do already but I add a level of play to make it seem fun to check out new things and also train her to protect on commend but that is a whole different thread) to see that nothing was there and thus no reason to be freaked out.

In short just OWN the situation not act it and not feel it. They will respond to what ever you do and in the end it's your dog and I can only tell you what has worked for me (did this with a Rotti, mastiff x terrier, and now my english mastiff) and I can say that Bella is MY shadow.

Also remember that for the past 14 months she was with a different pack. Mastiffs are LOYAL dogs and this is all new to her and she is just starting to get used to it. Remember that the last time she was dragged outside she left for good. Now you take her out and there is commotion  coupled with the fact that she really doesn't feel comfortable with you  or the situation and you get what you got. They are slow to do anything and it just might be a matter of time before she warms up to her new situation but she will as long as you make the extra effort.