First, thanks for that. I, too, have been dissatisfied with various definitions--including ones I have devised.
If I may, I do think we can distinguish between a process and a system. The economy is a process; an economic system is the set of institutions via which that process transpires (which is where money, among other things, enters the picture). Any study of an economy must take into account the pertinent economic system. A definition of the economy as a process must be specific enough to set definite parameters yet general enough to accommodate any imaginable set of institutions--which I see yours does.
The 'working definition' I use for the economy is, 'the production/acquisition of goods/services'.
Obviously, I disagree that "'goods and services' can be shortened to just 'resources'.” I think of resources as being elemental to production and acquisition--whatever might be necessary for either. [I like the slashes because the boundaries within the two sets of categories can be indistinct.]
But then, everything I think about is influenced by Warren J. Samuels's analysis of "social power" as 'the ability to effect choices'. The economy is nothing but choices being effected. In effecting choices we operate out of "opportunity sets," which are ad hoc combinations of the resources at our disposal that are pertinent to attempting to bring the choice at hand to fruition.