If the landlord chose to call the deposit a "security deposit" on the lease, not an "application fee", "holding deposit", or anything similar, then it's a security deposit and must be treated as such. As there was an understanding that you had not yet entered into a lease, but would likely do so at a later date, your landlord has not positioned himself to claim that there was an oral lease.
Quote Quoting Texas Property Code, Sec. 92.102. Security Deposit.
A security deposit is any advance of money, other than a rental application deposit or an advance payment of rent, that is intended primarily to secure performance under a lease of a dwelling that has been entered into by a landlord and a tenant.
Quote Quoting Texas Property Code, Sec. 92.103. Obligation to Refund.
(a) Except as provided by Section 92.107, the landlord shall refund a security deposit to the tenant on or before the 30th day after the date the tenant surrenders the premises.

(b) A requirement that a tenant give advance notice of surrender as a condition for refunding the security deposit is effective only if the requirement is underlined or is printed in conspicuous bold print in the lease.

(c) The tenant's claim to the security deposit takes priority over the claim of any creditor of the landlord, including a trustee in bankruptcy.
I have no way of telling you if the landlord will be more receptive to your "formal letter" than to your oral requests. If you think a letter might inspire him to return the money, all it costs you is some paper, and envelope and a stamp.

You can try to convince a court that he is acting in bad faith and to apply a multiplier to the damages; I am not going to try to guess what a court is going to decide under the facts that are presented at trial. You should anticipate that your recovery will be limited to the actual amount of the deposit, and treat anything more as a happy surprise.

But maybe you'll be lucky, he'll find a tenant, and all of this will be moot.

No, $700 is not a great deal of money for a holding deposit on a unit with a $1,400 rental rate. But from what you've told us, it's not a holding deposit.