Sorry to be so late to this particular discussion but I only just saw it whilst searching for 555 circuits.
I think it worthwhile adding my contribution as no-one has suggested my solution and someone in the future may find it handy.
The reason it's usually impossible to get a 1:1 mark:space ratio from a 555 is that the capacitor is being charged via the two resistors in series but only discharged via one of them. There are various solutions involving using diodes and / or transistors but all those have the unwanted side-effect of causing the frequency to vary with supply voltage.
My solution is very simple and needs just one component. All that is required is to change the threshold voltages for pins 2 and 6 of the 555. In astable mode the timing capacitor on pins 2 & 6 of the chip charges to the upper threshold (pin 6) and is then discharged to the lower one (pin 2) which starts the next cycle.
Those thresholds are set by a chain of 3 equal resistors (nominally 5kΩ) within the 555 chip. The upper threshold is 2/3 Vcc and the lower one half that.
As the upper threshold is exposed at pin 5 it can easily be manipulated using a resistor. Pulling it lower shortens the 'output high' part of the waveform without changing the 'output low' part.
In my experiment I used equal resistors for R1 and R2 (10k). With equal resistors pin 5 needs to be pulled down from 2/3 Vcc to about 4/9 Vcc (~0.44 Vcc) in order to equalise the high and low parts of the waveform. To achieve this a value of around 7k2Ω is needed for Rv.
The 555s internal resistors are well matched but may not be precisely 5kΩ so I suggest using a variable resistor for Rv so that an exact 1:1 ratio can be set.
The resulting waveform is very stable with regard to frequency and mark:space ratio when the supply voltage is altered.
Please note that the CMOS 555 chips have much larger values for their internal resistors so, although this technique should still work, a much larger value of Rv will be necessary.
The above circuit is not intended to produce the 2700Hz requested by the OP but could do so with the timing capacitor or resistors changed (e.g. 100n and 2k7).