At 2 1/2 months, he's still really too little to be very consistant for long. For most babies, they will have a sleeping pattenr that might last a week or two and then something will change. Many babies will get better around 6 months. I wasn't so lucky. Mine seemed to settle into longer patters as they approached 1 year and even more consistant patterns around 18 months.
I think your best bet is to ignor the clock and try to notice his cues. As soon as you notice him getting sleepy, help him along, whether that be rocking, singing, white noice, whatever seems to help. If nursing him seems to wake him up, you could try nursing him before bath and then helping him to fall asleep after you dress him. Try to play around with things and find something that works for him.
By the way, I love the way the bed time bath products smell, but I haven't actually found them to help my kids fall asleep. Just my experience.
Good luck! It really will get easier!