Start moving all of your non-1099/etc expenses on to one or a small set of corporate cards. (They can be in your own name or that of the LLC; the main requirement is that they not have personal expenses on them. This is to simplify bookkeeping.) If your contractors routinely need reimbursements for e.g. purchasing SaaS to do their jobs, start using Expensify. Your goals here are a) collecting a receipt for everything in a fashion organized well enough to find any receipt the IRS queries you about and b) not failing to record any business expense. The impact of failing to record a business expense is you, personally, pay your marginal income tax rate on that expense -- that can be a painful hit. (Your marginal rate will plausibly be 50%+ when you add self-employment tax, NY income tax, and US income tax, so missing a $2k hotel stay is a $1k error for want of a minute worth of data entry.)
Get an accountant, preferably one who works with other services firms (working with other devshops or design firms is a bonus but I'd not consider it a requirement). The first thing you'll ask the accountant to review is whether your 1099s will pass muster as 1099s. Major recurring questions to ask accountants include "Does our cash flow support adding a new team member right now?" and "How much should we have sitting in the bank ready for next April when taxes are due?"
Some of the financial advice I'd give sounds less like financing and more like proper business management of a consultancy, like "charge more", "make sure you're charging clients at least 3X what you're paying your contractors", "aggressively solicit referrals and follow-on work", "offer clients a monthly retainer agreement to maintain their projects at a slight discount to your day rate on a use-it-or-lose-it-basis; this will give your shop some recurring revenue to smooth out consulting cashflow swings", and "build pipeline, build pipeline, build pipeline."
See also this comment, which I think might be the most instrumentally useful one on HN: https://news.ycombinator.com/item?id=4247615
Good luck.