Australian with German Residence Permit... Schengen?

Caveat: IANAL so I may be misinterpreting things and getting things wrong where we enter legal territory.

As a legal resident of an EU member state you appear to have two sets of rights: one that derives from your status as the spouse of an EU national, which allows you to exercise full Freedom of Movement rights when travelling with your spouse and one that derives merely from your status as a legal resident of a Schengen area EU country. The second one is, for example, referenced in the Commission’s FAQ document (Question 15) or on the Czech Republic’s Ministry of the Interior webpage. There is no indication on either sites that these advantages are only applicable to Schengen residents without an EU spouse. Thus, I conclude you can visit any other Schengen area country in accordance with the 90/180 day rule.

Usually I would stop here but your circumstances are complex due to the fact that you used up 90 short stay Schengen days in total and in theory before receiving your German residence permit. At first sight, this appears to imply that you may have used up your Schengen days and would need to wait out the ticking of the 90/180 clock. However, Australia has bilateral agreements predating the Schengen agreement – and not only with Germany but also with France and Spain. Thus, you can use your 90 days in France, followed by 90 days in Germany, followed by another 90 days in France, followed by 90 days in Spain, followed by a third 90 days in France. As these agreements are rather old, I wouldn’t be surprised if they are not on the officials’ radar, so it is best to find or request some sort of confirmation that you can present on request to the border.

It seems that France has submitted and extended temporarily reintroduced border controls at its Schengen borders. I have not crossed a land border into France (or out of it) for quite a while now but I do not recall reading much about these controls. I don’t know how systematically or unsystematically they are being performed. I think it is entirely possible for you not to run into a border check on either leg of your trip unless if you’re taking trains to get to Spain. So you might not have to worry at all (but better be prepared than sorry).

You are operating under a couple of misconceptions.

As an Australian citizen I am granted an extra 90 days in Germany ON TOP of my Schengen travel, as long as that stay is at the end of my journey.

...and...

I have spent 22 days on the Schengen Clock, which 'paused' when I entered Germany due to the bilateral agreement.

No. Bilateral agreements allow you to extend your stay, but they do not pause the "regular" 90 days. So an Australian can go to Germany for up to 90 days after spending 90 days in a country without a bilateral agreement, but the reverse is not true: after spending 90 days in Germany, you cannot go to a country without a bilateral agreement (but you could go to a second country that does have a bilateral agreement. That's what is meant by "as long as it is at the end of your journey."

The thing that does pause the Schengen clock is the residence card. Whenever you're in Germany and in position of a German residence permit, the clock is paused.

So actually you used up your 90 days in the period between June 4 and September 3 (actually 89 days). You don't have 68 days available.

As a Non-EU family member, my German residence permit only allows me freedom of movement if I am travelling with my EU spouse, or meeting him at my destination.

...and...

This [68 days (that you don't actually have)] can be used independently of my German Residence Card that says I can only travel freely with my EU spouse

Your residence card counts as a "residence permit" under the Schengen codes, which means that it allows you to travel to other Schengen countries for up to 90 days in any 180-day period. That's if you're traveling without your spouse. When you're with your spouse, you fall under the free movement rules, and the Schengen 90/180 rule does not apply.

This isn't much use to you as an Australian, however, since you have that ability already; the 90 days you get as an Australian citizen aren't separate. It's far more useful for someone from a visa-required country such as India. What is useful to you, however, is that it makes your passport stamps relatively meaningless. There's no easy way to know how much of your time was spent in Germany and how much in other Schengen states. So unless they have reason to suspect that you are actually residing somewhere other than Germany, they're not going to look past the fact that you have a residence card.

Although the German bilateral agreement with Australia is not separate from the "normal" 90 days, the French and Spanish bilateral agreements mentioned in the other answer are indeed separate, so really you should be fine. On top of that, even in the absence of any bilateral agreements, there would not be much to worry about. Nobody is going to question how long you have been in the Schengen area. If you are checked by police, they'll see your residence card and let you go on your way.