Running first-level GLM without sufficient null/fixation events

I’m working on a dataset that used a block design with many short TRs (in an attempt to optimize things down the line for MVPA, a la Coutanche & Thompson-Schill, 2012). However, the design doesn’t follow that paper exactly – there is only one block of one condition in each functional run, with no extended periods of fixation before or after. Within each TR (1750 ms) there is a fixation (750 ms) and an image (1000 ms). There is also a single TR of fixation at the beginning of every run, but other than those fixation crosses, there are no periods of no stimulus.

Is there any way to run first-level GLM analyses on a dataset like this? If, for example, I used 3dDeconvolve, the stim times would encompass the entire run (except the first TR, which seems insufficient for estimating baseline activity). Is there a way to subsample to take advantage of the brief fixation in between each stimulus, or are those too short?

Any help is greatly appreciated.