I'm not a teacher
It's like a passive version of a causative construction "get sb to do sth", e.g. -----He (causer) got his gardener (causee) to mow the lawn.----- The causee understands his role but he's unwilling to perform it and it has to be overcome, so to speak. This is not the case with "have". If you said -----he had his gardener mow the lawn-----, it would mean there's no negotation. The gardener understands his role and he just does his job.
So, similarly, from your sentence it could be understood that you're trying to arrange for the shopping to be done and it's not going as smoothly as you'd want it.
Having said that, I think there might be another interpretation. For example, when you say -----I will get it organised----- the causer and causee are the same person: I. So, it's like you're saying, "I will tell myself to do it".
Also, 'try' in your sentences seems to emphasise even more that there's something in the way, or that you're not willing to go shopping.