It sounds as if your spit knot is similar to one of the ones I use. However what I do is take the end between my left thumb & forefinger, wrap the thread around the forefinger so it is a complete circle and then using the thumb I roll the thread off my finger twisting the two 'lays' of thread together. I then catch the loose knot between my middle finger and thumb and pull the thread tight (the right hand has been holding the threaded needle all along).
The other method I use was taught to me by my Mum and by hers ( which I was told was how the professionals did it), and is the one I taught to 5yrolds. You take your threaded needle in the right hand with the point facing the left hand. With the left hand catch up the end of thread to be knotted and lay it along the length of the needle with the cut end next to the eye, to make a nice circle. Wrap the thread around the needle several times (I always taught 6 times but find for myself that I usually only take 4 wraps). Then holding onto the wraps gently between the thumb and forefinger of the left hand, take hold of the pointed end of the needle and pull it through until you cannot pull it any further.
The method I was taught at primary school was the most annoying, and that was to make a loop in the end and pass the end through once (an overhand knot) then to repeat it and try to get the second knot on top of the first - never had any luck getting the second knot anywhere near the first knot as I recall
although I would probably do better these days, but by the time I had though about it I will have wrapped the thread around my left forefinger and rolled the knot off without thinking
Finally
although there could be other methods we've missed you can just take a couple of stitches without a knot, in the area that you are about to stitch over and catch down the end as you go, I usually do this for embroidery.