Paying rent, etc. with equity account and cash basis

I'm taking over my S corp's bookkeeping from a firm that handled it for me. The corp's reports are on a cash basis (or technically, the firm's year-end reports say "modified cash basis" with some fine print saying that checks are reported when they post to the bank feed). The corp's structure is very simple: single-owner (me), single-employee (me), a couple dozen transactions per month.

I noticed that for a few stray business purchases that I made with my personal credit card, in years past the firm reported these transactions as having paid out of an equity account that they called "Additional Paid-In Capital." This makes sense to me, and the company has never been audited due to this practice.

Can I continue my prior firm's practice and occasionally pay for things using this equity account? There are a few things that I'd like to expense but didn't necessarily pay for using the company's cash:

• Rent: I set up a home office last year and would like to treat it as a formal rental with a lease, etc. between myself as the lessor and the company as the lessee. No cash was exchanged--could I simply note the payments as credits from my company's equity account? Total amount: less than $5k.
• S corp owner health insurance premiums: As a 2% shareholder, I qualify for having my individual health insurance premiums reimbursed by the company. I understand that these amounts are W-2 wages--can I note that the wages were paid from equity? Total amount: less than $5k.

Since the company is on a cash basis, I can't just set up a liability account to pay things. The previous bookkeepers were OK with paying out of equity for various items, even expensive stuff like laptops. I don't want to make a habit of it, but these are legit expenses that I effectively paid for on the company's behalf and didn't think to pay myself for. It's tax time and I'd really like to deduct them, if possible.

Thanks!