‘Mutabilis’ is fertile to some degree; it often sets self-pollinated hips but rarely accepts other pollen. It’s pollen is almost useless on other varieties.
‘Safrano’ is workable as a pollen parent, but its offspring are often very pale in coloring. (‘Safrano’ itself is little more tham cream in color)
Several professional hybridizers have said to me in the past that any cross you want to try is as good as any other, at least up until you see the results. That is to say, anything you care to try is valid as long as you are willing to take a chance on the results. Some crosses using only the best parents available will result in nothing but junk, and some of the most unlikely roses when mated will produce some spectacular results. I’m sure I’m not the only one who will tell you that the more unlikely the mating, the greater your chances of getting something interesting.
Some very useful pollen parents I have worked with include: ‘Abraham Darby’, ‘Little Chief’, ‘Magnifica’(very similar to ‘Hansa’), ‘Magic Wand’, ‘Mary Rose’, ‘Buff Beauty’, ‘Scarlet Moss’, ‘Fairy Moss’, ‘Out of Yesteryear’, ‘Tradescant’, ‘June Laver’, and ‘STW-1’(a Ralph Moore stud cultivar now available from Sequoia Nursery).
It is most useful to do research to find out what roses have served as successful parents in the past and start work with some of these. It is also very important to have some idea of what results you want before you start making parent choices. If you choose to try roses like ‘Mistress Quickly’ for breeding, you may find out that they are unsuitable for breeding and you must be prepared to abandon them as such. Hybridizing takes years and years of work to start getting meaningful results, and you cannot afford to continue pursuing difficult and unworkable roses, IMHO.
‘Trier’ is a worthwhile plant to try as a parent, as it was this rose that started the Pemberton Hybrid Musks. Several of the Austin roses are very worthwhile, especially the ones that already have a track record for performance as parents.
I concur that ‘Old Blush’ is worth exploring as a parent, either as a female or a male parent. (Better as a male, generally)
I have chosen to work last season with ‘Crepuscule’ also, with the idea that remontant climbers will result. I have yet to see the first offspring yet, so cannot comment on its worthiness as a parent. However, it is a VERY willing pollen parent, setting seed easily on many parent varieties.
As for ‘Hansa’ as a parent; many people have tried working with it and often the seedlings are not worth keeping. I know that ‘Magnifica’, a very similar Rugosa has been used with very good results and may be more worthwhile pursuing.
If it were me testing ‘Mistress Quickly’ as a seed parent, I would use ‘Little Chief’ on it first, as the chances are that something interesting may result. ‘Crepuscule’ may be worth trying too, but you can be pretty much assured that you will lose the apricot coloring unless you mate ‘Crepuscule’ with another strong yellow/orange rose.