You could use it however you want. I know that your approach is different then mine, so you would use in a way that makes sense to you.
If you don't have the exact time of birth, then you cannot look at houses. Often people will say 'I was born in the morning' or some unknown time. That is useless. If they don't know the exact time then you can't use vague information to set up a chart. But you can look at the aspects between the planets, and that is a big part of the picture.
I set up a noon chart because you want to know the relative position of the moon and what sign it is in. The moon moves fast, about 8 degrees a day. With a noon chart you know that the moon is within approximately 4 degrees of the placement that is shown on the noon chart and hopefully you can determine the sign and the aspects will be close enough to get a good picture. The main thing I look at for the manipulation is the aspects. For example, I don't usually use asteroids but I might if someone needs a blue line, and an asteroid can be found to provide support.
I use Astro,com extended chart selection because are many options available. In that format the squares and oppositions are red, and the sextiles and trines are blue. I mostly care about how the planets interact with each other. Who are the friends and foes and how can I make them get along.
I do know astrology and I observe the rules as I understand them, but subconsciously I know more then I can comprehend so by using the chart as a mandala you are working with the energy both consciously and subconsciously.
That is basically how I use it for magic. As for interpretation and synthesis I would look at what is interesting to me. Some charts are frankly boring and I don't care anything about where their planets are, while i find other charts to be very interesting.
With just a sun sign/age I don't invest much energy into that. I will look at the ephemeris to see approximately where their planets are and I don't even draw up a chart.
If I had nothing at all, I could use a horary technique and look at the chart of the moment. Really I am not good at horary but I know the simple rules. One of the accepted rules is that the chart is erected for the time the astrologer receives the question. I could look at that chart and treat it as a horary. This is just to absorb the energy, and the act of simply thinking about it is 'doing something'.
Another trick is to use a composite chart to combine the energies of 2 people...I personally don't use a Composite chart much for interpretation. I don't care about it but combining the energy of 2 people, is a symbolic way to do that.
These techniques work for me because I was taught to use it this way. As you probably are aware I am one who was entirely taught from within. My guardians trained me so they will honor the techniques that we use and facilitate the 'magic'...Of course I had to study and learn in the usual way but the way I apply is as I was taught.
I don't use the astrology for timing usually. Occasionally I will do something when an aspect in the sky is exact if it feels important. If timing is a concern I would pay attention to the current planetary conditions.
This is just one tool I use. It is useful in many different ways. When you are doing a spell and you want to work with a person that you have never met and you have no name or information except their birthchart then you have their unique energy signature. That is useful. I am sure that you don't need anything to know exactly who you are working with. I don't either. I know who they are and can single them out without any information except the knowledge that 'that is them'..but the astrology is better then any other identifying information.
If I wanted to correct neptune energy, which is Pisces or the 12th house, I would use Saturn. Neptune dissolves, Saturn rebuilds. I always want to find a Neptune/Saturn connection because the Neptune needs the structure that Saturn provides. So I would try and find a connection.
When looking at transits sometimes the picture is bleak, but you can see when things will get better, and find a way to look on the bright side. I might make a suggestion and say 'that sucks but you have that planet well placed in your natal chart so you can handle it"..By making that suggestion then it inspires the planetary energy of the native to step up to the plate and do it's duty as per the natal promise.
Some of this might sound off the wall and maybe it is, but it works for me. It could work for you and I am sure you would develop your own system that has the integrity that you require.